Contracting/expanding self-sealing cryogenic tube seals

ABSTRACT

Contracting/expanding self-sealing cryogenic tube seals are disclosed which use the different properties of thermal contraction and expansion of selected dissimilar materials in accord with certain design criteria to yield self-tightening seals via sloped-surface sealing. The seals of the subject invention are reusable, simple to assemble, and adaptable to a wide variety of cryogenic applications.

The subject invention was made with government support under a researchproject supported by NASA-Kennedy Space Center and under Contract No.NAS10-11569 and Research Grant No. NAG10-0083. The government hascertain rights in this invention.

BACKGROUND OF THE INVENTION

The rigorous conditions of very low operating temperatures coupled withhigh pressure impose extreme difficulties for controlling cryogenleakage from in-line tube fittings. The KC126 fitting, which has beenused by NASA in the fuel lines of the space shuttle, has been found toleak. We have shown that the KC126 fitting leaks at 205K, and at 77K hasa leak mass flux of 1.28×10⁻³ kg/min. See also Moore, Z., D. Capellin,A. Rodriguez, J. England (1988) "LH₂ TSM Leakage Problem," InterimReport: DM-MED-4, NASA, J.F.K. Space Center. Accordingly, there exists aneed for an improved design of cryogenic seal for tube fittings such asthose used in the space shuttle, and which is reusable and seals underextremes of low temperature and high pressure. Such a seal would havewide application in the cryogenic art.

The problem of sealing a joint between two interconnecting pieces thatare designed to operate at cryogenic temperatures has been previouslyrecognized. In part, this problem was addressed in U.S. Pat. No.3,630,533, issued Dec. 28, 1971 to Butler et al., entitled "Dynamic Sealfor Cryogenic Fluids." An additional problem addressed by Butler et al.is the high temperature sealing problem, which influenced Butler etal.'s design. Butler et al. used a circular sealing ring made from afluorocarbon plastic material to seal two metal tubular couplings. Thesealing ring is pressed onto a radially outward surface of one of themetal couplings. The sealing ring has a radially inward protrudingannular rib which elastically and inelastically deforms as the sealingting is pressed into place. This arrangement effects a sealingengagement between the sealing ting and the metal coupling attemperatures reported to be within the range of 70° F. to -423° F. Atnormal temperatures, the inner surface of the sealing ring is held insealing engagement by the elastic preload induced by the initialinterference press-fit and deformation of the protruding annular rib. Inaddition to the preload, a circumferential tension is generated in thesealing ring as the temperature decreases, because the sealing ring'scoefficient of thermal expansion and contraction is greater than thecoefficient of thermal expansion and contraction of the metal couplings.Thus, because of the differences in the expansion coefficients of thesealing ring and the metal coupling that it is pressed onto, the sealingengagement between these members of two different materials becomestighter as the temperature decreases. However, in Butler et al.'sdesign, each time two metal tubular couplings are sealed together, thecomplex plastic sealing ring must be inelastically deformed into aparticular configuration. Since the sealing ring is irreparably deformedby its installation, after separation of the two couplings formaintenance or other reasons, it is necessary to replace the sealingring before the two couplings can be rejoined. Such a "use once andthrow away" approach is wasteful, ultimately expensive, and troublesomeif a replacement ring is not readily available. A coupling between twomembers which can be joined and separated, without requiring a newsealing ring each time, is needed.

BRIEF SUMMARY OF THE INVENTION

The subject invention, contracting/expanding self-sealing cryogenic tubeseals, are thermal-contraction controlled-action sealing and grippingdevices which utilize the differences of the thermal contraction ofselected dissimilar materials in a specially designed and composedstructure to self-tighten the seal via sloped-surface sealing betweencoupled members as the temperature decreases from ambient temperature."Sloped-surface sealing" means that the contact points creating the sealare not the result of contact of parallel surfaces. In one preferredembodiment, the cooling process causes the contraction of a sealingspacer, further gripping the member ends, and causes the contraction ofa housing nut, further forcing the coupling member ends together,thereby taking advantage of sloped-surface sealing in a novel way andpreventing leakage of the flowing cryogen.

The contracting/expanding self-sealing cryogenic tube seals areleak-free from room temperature to cryogenic temperatures as low as thatof liquid helium and, unlike anything known in the art, provide easilyremountable tube connections for high pressure and low temperatureapplications.

The contracting/expanding self-sealing cryogenic tube seal is a generalpurpose cryogenic tube seal. It provides reliable leak-free connectionsfor the low/high pressure and low temperature working conditions incryogenic applications. It can be easily applied to various cryogenicfittings and valves. Some basic advantages of contracting self-sealingcryogenic fittings are summarized as follows:

1. Applicable to any low temperatures and temperature cycling.

2. Works on most common magnetic/non-magnetic tube materials.

3. Seals on machined surfaces.

4. Does not reduce the flow area.

5. Works on vacuum as well as low or high pressures.

6. Simple in structure for production and handling.

7. Easy to use, similar to the standard SAE fittings.

8. Easy to assemble and disassemble.

9. Ability to reuse without special maintenance or replacement.

10. Not sensitive to the applied coupling torques.

11. Not sensitive to the moment from other components.

12. Not corrosive for common cryogen.

13. Applicable to most cryogenic tube connections.

Design criteria for contracting/expanding self-sealing cryogenic (CESSC)tube seals are taught which must be applied in accord with the subjectinvention, and which depend on the properties of selected materials aswell as the configuration of the seal. These criteria, illustrated bythe following examples, enable the construction by means well known inthe art of a tremendous number of varying embodiments, all of which arebased on the novel sloped-sealing concepts taught herein, as will bereadily apparent to the skilled artisan.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a longitudinal section through a preferred embodiment ofa contracting self-sealing cryogenic tube seal.

FIG. 2 depicts a longitudinal section through a variation of theembodiment depicted in FIG. 1, wherein the O-ring spacer has beenreplaced with a modified spacer.

FIG. 3 depicts a longitudinal section through an alternative embodimentof a contracting self-sealing cryogenic tube seal having only threecomponents.

FIG. 4 depicts a longitudinal section through an alternative embodimentof the contracting self-sealing cryogenic tube seal.

FIG. 5 depicts the geometric analysis of cryogenic shrinkage of thecomponents of the contracting self-sealing cryogenic tube seal.

FIG. 6 is a graphic representation of the design criteria for thecontracting self-sealing cryogenic tube seal.

FIG. 7 depicts a longitudinal section through a preferred embodiment ofa contracting/expanding self-sealing cryogenic tube seal.

FIG. 8 is a schematic drawing of an H-shaped spacer of a preferredembodiment of the contracting/expanding self-sealing cryogenic tubeseal.

FIG. 9 depicts an H-shaped spacer of the contracting/expandingself-sealing cryogenic tube seal wherein the sloped surface sealing isaccomplished via contact of curved surfaces.

FIG. 10 is a schematic drawing of a preferred embodiment of a couplingmember of the contracting/expanding self sealing cryogenic tube seal.

FIG. 11 is a schematic drawing of a preferred embodiment of the housingnut of the contracting/expanding self sealing cryogenic tube seal.

FIG. 12 depicts various embodiments of the contracting/expanding selfsealing cryogenic tube seal in potential operational configurations.

Table 1

DETAILED DISCLOSURE OF THE INVENTION

Following are examples which illustrate procedures, including the bestmode, for practicing the invention. These examples should not beconstrued as limiting.

EXAMPLE 1 A Preferred Embodiment

In a preferred embodiment, as depicted in FIG. 1, the contractingself-sealing cryogenic tube seal consists of four basic components:metal coupling members 1 and 2, each having a male an-flare tube end 14and 15, respectively, an O-ring spacer 3, and a housing nut 4.. Housingnut 4 comprises internal threads 13 for threaded engagement withexternal threads 5 and 6 on coupling members 1 and 2, respectively. TheO-ring spacer 3 rests between two male an-flare coupling members 1 and2.

Various parts of contracting self-sealing cryogenic tube seals are madeof dissimilar solid bar metals, thereby taking advantage of theirdifferent coefficients of thermal contraction. The materials for O-ringspacer 3 and housing nut 4 have higher values of the coefficient ofthermal contraction than does the material used for coupling members 1and 2. In the preferred embodiment, the components are axisymmetric(symmetric about an axis).

Assembly of the contracting self-sealing cryogenic tube seal depicted inFIG. 1 is a simple matter of engaging housing nut 4 with coupling member1 until the an-flare tube end 14 of coupling member 1 is positionedapproximately in the middle of housing nut 4, proximal to the lateralplane represented by segment FG. O-ring spacer 3 is then inserted intohousing nut 4 until it contacts an-flare tube end 14 of couplingmember 1. Coupling member 2 is then engaged into housing nut 4 untilan-flare tube end 15 is secured against O-ring spacer 3. The slopedsurface of the an-flare tube ends allows for contraction of the spacerwhile ensuring that a tight seal is maintained.

In operation, cryogenic fluid begins to flow through the contractingself-sealing cryogenic tube fitting along longitudinal axis ST asdepicted in FIG. 1. For ease of discussion, movement toward position Swill be referred to as "upward" and movement toward position T will bereferred to as "downward;" movement toward axis ST will be referred toas "inward" and movement away from axis ST will be referred to as"outward." As the cryogenic fluid flows, the temperature of all parts ofthe contracting self-sealing cryogenic tube seal begins to decrease.Accordingly, the various parts of the tube seal shrink in size. Contactportion 10 at tube end 14 tends to shrink upward and inward. Contactportion 11 at O-ring spacer 3 tends to shrink downward and inward. Thatportion 18 of housing nut 4, which is depicted above lateral plane FG,tends to shrink downward and inward, while housing nut portion 19, belowplane FG, tends to shrink upward and inward. Because O-ring spacer 3 andhousing nut 4 are made of materials having a larger coefficient ofthermal contraction than are coupling members 1 and 2 (and thus tubeends 14 and 15), the inward shrinkage of O-ring spacer 3 tends to causeit to press even more tightly against tube ends 14 and 15. Similarly,shrinkage of housing nut 4 tends to force tube ends 14 and 15 towardeach other, as well as providing a tighter engagement of threadedportions 13, 5, and 6. Thus, the effects of thermal contraction willalways maintain a leak-free seal in the contracting self-sealingcryogenic seal.

EXAMPLE 2 Some Alternative Embodiments

FIGS. 2, 3, and 4 depict exemplary alternative embodiments of thesubject invention. To ensure proper sealing, contact surfaces of thecomponents are axisymmetric. FIG. 2 depicts an embodiment similar tothat depicted in FIG. 1 except that O-ring spacer 3 has been replacedwith a flared spacer 27 having opposed female-flared contact surfaces 28and 29, each having a complementary shape to tube ends 14 and 15,respectively, such that a tight seal is maintained therebetween inaccord with the design criteria described hereinafter.

FIG. 3 depicts coupling member 1 with male an-flare tube end 14,coupling member 21 with female flare tube end 22, and housing nut 20,having a large bore at one end with internal threaded means forreceiving and engaging coupling member 1 and a smaller (step down) boreat the other end, which is just large enough to surround coupling member21, but not large enough to allow female flare tube end 22 to passthrough. The internal surface of the step-down end of housing nut 20defines a circumferential flange 23, radially sloping downward andoutward. Housing nut 20 engages coupling member 1, and as housing nut 20is tightened about coupling member 1, flange 23 engages acircumferential lip 24 on coupling member 21, lip 24 having acomplementary slope to that of flange 23 such that contact is maintainedbetween lip 24 and flange 23, and pulls coupling member 21 such that thefemale flare tube end 22 of coupling member 21 is thereby brought intocontact with male an-flare tube end 14 of coupling member 1, similar tothe method by which a garden house is brought into contact with aspigot. Secured contact between tube end 14 and tube end 22 is therebymaintained in accord with the disclosed design criteria. To maintain thesloped-surface seal of this embodiment leak-free at cryogenictemperatures, coupling member 21 and housing nut 20 are made ofmaterials having a larger coefficient of thermal expansion than thematerial of coupling member 1, all in accord with the design criteria.For example, coupling member 21 and housing nut 20 may be made ofcopper, if coupling member 1 is stainless steel.

The embodiment depicted in FIG. 4 combines features of the embodimentsdepicted in FIGS. 1 and 3. Housing nut 4 is engaged with coupling member1 until the an-flare tube end 14 of coupling member 1 is positionedapproximately in the middle of housing nut 4. Housing nut 4 then engagescollar 25, which has external threaded means for being engaged andsecured by the internal threaded means of housing nut 4, and which alsohas a wedge end 26 which engages lip 24 on coupling member 21 and forcesfemale flare tube end :12 into secured contact with male an-flare tubeend 14. Thus, it can be seen that the collar and wedge component of thisembodiment can be used with housing nut 4 to effectively replace theflange 23 and small bore end of housing nut 20 of the embodimentdepicted in FIG. 3. To maintain the sloped-surface seal of thisembodiment leak-free at cryogenic temperatures, collar 25 (having wedgeend 26), as well as coupling member 1, are made of materials having asmaller coefficient of thermal expression than the material of housingnut 4 and coupling member 21 (having lip 24).

EXAMPLE 3 Design Criteria of Contracting/Expanding Self-SealingCryogenic Seals

According to the theory of Gas Dynamics and the linear analysis ofthermal contraction, some criteria for the design ofcontracting/expanding self-sealing cryogenic seals are given below:

(1) Design criteria for two components--tube and spacer: ##EQU1##

(2) Design criteria for three components--housing nut, tube-end, andspacer: ##EQU2##

Referring to FIG. 5, α is the an-flared angle of the tube ends. β is theradius ratio of O-ring spacer r₁ /R. λ is the ratio of the thickness oftube-end to the radius of the spacer, w/R. γ_(o) (γ_(o) =ε_(o) /ε_(p))is the ratio of thermal contraction of the material used for the spacerto that of the tube ends. γ_(h) (γ_(h) =ε_(h) /ε_(p)) is the ratio ofthermal contraction of the material used for the housing-nut to that ofthe tube ends. The parameters, α, β, and λ, are the parameters of theseal geometry. γ_(o) and γ_(h) are the functions of temperature, whichcan be found from the tables of material properties and are well knownin the art.

These criteria have been illustrated in the graphs of FIG. 6. Thephysics of the thermal contracting process or the thermal and geometriceffects of the contracting/expanding self-sealing cryogenic seal isrevealed by these criteria. The contracting/expanding self-sealingcryogenic seal is predictable in its response to temperaturefluctuations--it consistently fulfills the promise of self-sealing forcryogenic applications.

A linear approximation of the sealing process in a thermal-contractioncontrolled-action seal by a simple geometric analysis was used tocalculate design parameters of the contracting/expanding self-sealingcryogenic seal. The contracting self-sealing cryogenic tube sealsexemplified herein were designed in accord with this analysis and havesuccessfully passed a series of tests in the cryogenic leak test systemwith a temperature drop from room temperature down to the liquid heliumtemperature in the Cryogenic Laboratory of Florida Atlantic University.

Shown in FIG. 5 is the cross-section of an O-ring spacer seated betweenan-flared tube ends with axial angle, α, before and after coolingperiod. Both O-ring spacer and tube end, which have differentcoefficients of thermal expansion, shrink axisymmetrically in thecooling process. A₁ and A₂ are two contact points of the mating partsbefore and after cooling. Because of the thermal contraction, theoriginal contact point, A₁, in the tube end moves to D, with a radialshrinkage, Δt=A₁ E, and an axial shrinkage, ΔL=ED.

A maximum value of the shrinkage of the tube end in axial direction, ΔL,can be obtained if presuming a zero-thermal-stress condition, whichmeans free contracting of both O-ring spacer and tube end without losingcontact with each other. It is apparent that if the actual axialshrinkage of the tube end is larger than the zero-thermal-stressshrinkage, ΔL, the contracting self-sealing cryogenic seal will neverachieve a leak-free seal.

From the geometry in FIG. 5, if we let ΔL'=A₁ B and Δt'=A₁ C, then##EQU3## and Δt'=ΔL' tana, we have ##EQU4## and also,

    ΔL' sin α+r.sub.1 =ΔR cos α+r.sub.2

we have, ##EQU5## where Δr=r₁ r₂. Combining Eq. (1) and (2), ##EQU6##

Assuming a linear contraction as a first approximation, i.e., ΔR=ε_(o)R, since r is much smaller than R, and Δr=ε_(o) r₁ and Δt=ε_(p) (R-r₁cos α) for the same approximation, where ε and ε_(p) are thecoefficients of thermal expansion of O-ring spacer and tube end,respectively. Substituting ΔR, Δt, and Δr into Eq. (3), we have,##EQU7## Let γ=ε_(o) /ε_(p), and β=4₁ /R, we can rewrite Eq. (4) as##EQU8##

The maximum axial shrinkage of tube end, ΔL, from the above equation, isa function of three parameters, α, β, and γ, where α is the an-flaredangle of the tube end, β is the radius ratio of the O-ring spacer, and γis the ratio of thermal properties of material used for two matingparts.

In order to have a positive value of ΔL, the term in brackets must bepositive, which leads to three design criteria for three parameters,each one depending on the other two, which are given as follows:##EQU9##

According to the above criteria, α and β do not have lower limitationsexcept for the negative values, which are meaningless for an O-ringseal. The lower limitations actually depend on the strength of thematerials. The minimum value of α depends on the requirement for thewall thickness of the tube end. The minimum value of β depends on therequirement for the radius of the cross section of the O-ring spacer.The graphs of FIG. 6 represent possible values for α, β, and γ that canbe used for the design of contracting self-sealing cryogenic seal. InTable 1, a dimensionless parameter of ΔL/Rε_(p), is given which iscomputed from Eq. (5) for the convenience of applications. For example,if we choose α=35°, and β=0.3, then γ must be larger than 1.2. If wechose γ=6 (for copper O-ring and invar tube end), we have ΔL/Rε_(p)=4.5. If R=8 mm, and ε_(p) =0.06% (invar at 6K), the maximum promisingaxial shrinkage, ΔL=0.022 mm. This is an approximate value for thetested contracting self-sealing cryogenic seal at liquid heliumtemperature.

EXAMPLE 4 Selection of Materials for Contracting/Expanding Self-SealingCryogenic Seals

The function of a contracting/expanding self-sealing cryogenic sealrelies upon the differences of the thermal contractions of dissimilarmaterials in a specially composed structure which, in a novel,advantageous manner uses the concept of sloped-surface sealing. Theselection of materials is basically determined by the nature of thermalcontraction of the materials used for each of the components. Thecontracting/expanding self-sealing cryogenic seal works only if it isdesigned to meet the criteria which are dependent upon not only thethermal properties of materials, but also the geometric parameters. Theselection of the materials, therefore, is not an independent factor inorder to achieve a self-sealing purpose. It must be considered togetherwith the geometric parameters of the components of the seal. In thisregard, the contracting self-sealing cryogenic seal is an integratedunit.

One of the possible combinations is given as follows: The material fortube ends is commonly the same as that for the tubing bodies. Forcryogenic situations, stainless steel is a commonly-used material fortubing bodies. Therefore, among other common engineering materials, inthe embodiment depicted in FIG. 1, copper is one of the possible choicesfor the housing nut and the O-ring spacer, used with the stainless steeltube ends. However, the geometric configuration must meet thecontracting self-sealing cryogenic criteria disclosed above with thegiven parameter of thermal contraction ratio calculated for copper tostainless steel.

EXAMPLE 5 Test Results of Various Embodiments of ContractingSelf-Sealing Cryogenic Seal

The contracting self-sealing cryogenic seals have passed a series oftests in the cryogenic leak test system at Florida Atlantic University.The detailed information of the cryogenic leak test system is given inJia, L. X., D. Moslemian, W. L. Chow (1992) "Cryogenic leak testing oftube fittings/valves," Cryogenics 32(9):833-839, which is incorporatedherein by reference thereto. The tests were conducted under twodifferent temperature levels, LN₂ temperature (≈77K), and LHetemperature (≈4K).

For the leak test under LN₂ temperature, the highest internal pressureagainst the external vacuum applied to this seal has been 31×10⁵ Pa,nearly two times the working pressure in the space shuttle. The testlasted about ten hours without showing any signs of leak from vacuumgauges at pressure of 5×10⁻⁴ Bar within the sample chamber. In anothertest, initial pressurization was to 27.1×10⁵ Pa. As the temperaturedropped to 140K, additional gaseous helium was supplied to increase theinternal pressure from 12×10⁵ Pa to 26.2×10⁵ Pa. When the equilibriumtemperature of 77K was reached, internal pressure was reduced down to17.2×10⁵ Pa and kept under this condition for another 10 hours.Throughout the testing period, no pressure increase was detected in theevacuated sample chamber used to house the seal.

For the leak test under LHe temperature, a constant internal pressure of27.1×10⁵ Pa against the external vacuum was applied to the contractingself-sealing cryogenic tube seal. The test lasted 5 hours at thetemperature of 4.5K˜6.9K without showing any signs of leak from vacuumgauges at pressure of 1×10⁻⁶ Bar within the sample chamber. The tests onthe contracting self-sealing cryogenic tube seals at LHe temperatureindicated that it is feasible to develop a new series of cryogenic tubeseals for the LH₂ transfer lines of the space shuttle, as well as forother cryogenic applications, based on the novel sloped-sealingtechnology taught herein.

EXAMPLE 6 Contracting/Expanding Self-Sealing Cryogenic Seal

The concept for a contracting self-sealing cryogenic tube seal can beextended for a special application where a wide range and high rate oftemperature cycling is a significant feature of the working condition. Acontracting/expanding self-sealing cryogenic tube fitting isschematically shown in FIG. 7. With larger thermal contraction andthermal expansion coefficients, the shrinking or expanding displacementof the spacer caused by temperature cycling always tends to prevent theappearance of any possible leak gap between the tube ends and thespacer, no matter whether the working temperature is decreasing orincreasing. A similar analysis for a contracting/expanding self-sealingcryogenic seal can be easily obtained as described above by consideringan additional reverse thermal process of temperature increase.

In a contracting/expanding self-sealing cryogenic seal as depicted inFIG. 7, the spacer 30 has an H-shaped cross-section, having opposedV-shaped female sloped-sealing surfaces 31 and 32 at each end whichcontact the complementary sloped male an-flare tube ends 39 and 40,respectively, of the coupling members 37 and 38. The male angle of thetube end is made slightly larger than the female angle of thecorresponding surface of the spacer 30. A similar H-shaped spacer/sealis depicted in FIG. 9, wherein the sloped surface sealing isaccomplished by contact of curved surfaces. When temperature isdecreased, the outwardmost contact surfaces 33 and 34 of the spacer 30will tightly grip the tube ends 39 and 40. When temperature isincreased, the inside contact surfaces 35 and 36 of the spacer 30 willtightly press against the tube ends 39 and 40. Therefore, a tight sealis achieved under the temperature cycling condition. Since thetemperature changes in two opposite directions, the thermal behavior ofthe housing nut 41 no longer contributes consistently for tube sealingduring the temperature cycling. Therefore, in a preferred embodiment,the material for the housing nut 41 has a smaller coefficient of thermalcontraction (or expansion) than does the spacer 30. The material forcoupling members 37 and 38 also has a smaller coefficient of thermalexpansion than does that of spacer 30. The selection of materials forthe spacer 30 and tube ends 39 and 40 of contracting/expandingself-sealing cryogenic seals follows the same design criteria givenabove. In a preferred embodiment, the subject seal, seeminglysophisticated, surprisingly simply solves sometimes severe systemseepage substantially superior to standard space shuttle seals byspecially-selected, securely sandwiched, sloped-surface spacers snuglysurrounding stainless steel surfaces shown self-sealing by sequentialshrinking and swelling.

One preferred embodiment of the contracting/expanding self-sealingcryogenic seal was fabricated for use in the LH₂ lines of the spaceshuttle at the JFK Space Center. The H-shaped spacer 30 (see FIGS. 7 and8) has a larger thermal expansion coefficient than that of the tube ends39 and 40 between which it is sandwiched. Shrinkage or expansion of thisspacer always tends to prevent the formation of any possible leaking gapbetween the tube ends and the spacer, regardless of whether the workingtemperature is decreasing or increasing. The contracting/expandingself-sealing cryogenic tube seal provides leak-free and easilyremountable tube connections from temperatures as high as the componentmaterials can withstand to cryogenic temperatures as low as that ofliquid helium, and under pressures varying from vacuum to severalhundred psi or more. The seal is especially effective in applicationswhere a wide range and high rate temperature cycling are significantfeatures of the working conditions. The seal can be easily integratedinto all kinds of cryogenic tubing components, such as fittings andvalves. Several possible configurations which employ thecontracting/expanding self-sealing cryogenic tube seal are shown in FIG.12. The contracting/expanding self-sealing cryogenic seal has passed thetemperature cycling test: first cooled down from 296K to 12K, thenheated up to 300K within 20 minutes, and then cooled down again to 77K,while the pressure maintained 400 psig, without showing any sign ofleak.

It should be understood that the examples and embodiments describedherein are for illustrative purposes only and that various modificationsor changes in light thereof will be suggested to persons skilled in theart and are to be included within the spirit and purview of thisapplication and the scope of the appended claims.

                  TABLE 1                                                         ______________________________________                                        Design Parameters for CSSC Tube Fitting, (d1 = ΔL/Rε.sub.p).    ______________________________________                                        gama(beta = 0.1000000                                                                       alfa =  5) >   1.000848                                         gama        beta      alfa                                                    dl(    1.000848 0.1000000  5  )=   0.0000000E + 00                            dl(    1.500848 0.1000000  5  )=   5.141342                                   dl(    2.000848 0.1000000  5  )=  10.28268                                    dl(    2.500848 0.1000000  5  )=  15.42402                                    dl(    3.000848 0.1000000  5  )=  20.56536                                    dl(    3.500848 0.1000000  5  )=  25.70670                                    dl(    4.000848 0.1000000  5  )=  30.84805                                    dl(    4.500848 0.1000000  5  )=  35.98938                                    dl(    5.000848 0.1000000  5  )=  41.13073                                    dl(    5.500848 0.1000000  5  )=  46.27207                                    dl(    6.000848 0.1000000  5  )=  51.41341                                    gama(beta = 0.1000000                                                                       alfa = 10) >   1.003408                                         gama        beta      alfa                                                    dl(    1.003408 0.1000000 10  )=   0.0000000E + 00                            dl(    1.503408 0.1000000 10  )=   2.547703                                   dl(    2.003408 0.1000000 10  )=   5.095405                                   dl(    2.503408 0.1000000 10  )=   7.643107                                   dl(    3.003408 0.1000000 10  )=  10.19081                                    dl(    3.503408 0.1000000 10  )=  12.73851                                    dl(    4.003408 0.1000000 10  )=  15.28621                                    dl(    4.503408 0.1000000 10  )=  17.83392                                    dl(    5.003408 0.1000000 10  )=  20.38162                                    dl(    5.503408 0.1000000 10  )=  22.92932                                    dl(    6.003408 0.1000000 10  )=  25.47702                                    gama(beta = 0.1000000                                                                       alfa = 15) >   1.007736                                         gama        beta      alfa                                                    dl(    1.007736 0.1000000 15  )=   0.0000000E + 00                            dl(    1.507736 0.1000000 15  )=   1.672840                                   dl(    2.007736 0.1000000 15  )=   3.345681                                   dl(    2.507736 0.1000000 15  )=   5.018521                                   dl(    3.007736 0.1000000 15  )=   6.691361                                   dl(    3.507736 0.1000000 15  )=   8.364202                                   dl(    4.007736 0.1000000 15  )=  10.03704                                    dl(    4.507736 0.1000000 15  )=  11.70988                                    dl(    5.007736 0.1000000 15  )=  13.38272                                    dl(    5.507736 0.1000000 15  )=  15.05556                                    dl(    6.007736 0.1000000 15  )=  16.72840                                    gama(beta = 0.1000000                                                                       alfa = 20) >   1.013931                                         gama        beta      alfa                                                    dl(    1.013931 0.1000000 20  )=   0.0000000E + 00                            dl(    1.513931 0.1000000 20  )=   1.227548                                   dl(    2.013931 0.1000000 20  )=   2.455097                                   dl(    2.513931 0.1000000 20  )=   3.682646                                   dl(    3.013931 0.1000000 20  )=   4.910194                                   dl(    3.513931 0.1000000 20  )=   6.137743                                   dl(    4.013931 0.1000000 20  )=   7.365292                                   dl(    4.513931 0.1000000 20  )=   8.592841                                   dl(    5.013931 0.1000000 20  )=   9.820390                                   dl(    5.513931 0.1000000 20  )=  11.04794                                    dl(    6.013931 0.1000000 20  )=  12.27549                                    gama(beta = 0.1000000                                                                       alfa = 25) >   1.022151                                         gama        beta      alfa                                                    dl(    1.022151 0.1000000 25  )=   0.0000000E + 00                            dl(    1.522151 0.1000000 25  )=   0.9539434                                  dl(    2.022151 0.1000000 25  )=   1.907887                                   dl(    2.522151 0.1000000 25  )=   2.861830                                   dl(    3.022151 0.1000000 25  )=   3.815774                                   dl(    3.522151 0.1000000 25  )=   4.769717                                   dl(    4.022151 0.1000000 25  )=   5.723660                                   dl(    4.522151 0.1000000 25  )=   6.677603                                   dl(    5.022151 0.1000000 25  )=   7.631547                                   dl(    5.522151 0.1000000 25  )=   8.585490                                   dl(    6.022151 0.1000000 25  )=   9.539434                                   gama(beta = 0.1000000                                                                       alfa = 30) >   1.032636                                         gama        beta      alfa                                                    dl(    1.032636 0.1000000 30  )=   0.0000000E + 00                            dl(    1.532636 0.1000000 30  )=   0.7660255                                  dl(    2.032636 0.1000000 30  )=   1.532051                                   dl(    2.532636 0.1000000 30  )=   2.298077                                   dl(    3.032636 0.1000000 30  )=   3.064102                                   dl(    3.532636 0.1000000 30  )=   3.830127                                   dl(    4.032636 0.1000000 30  )=   4.596153                                   dl(    4.532636 0.1000000 30  )=   5.362179                                   dl(    5.032636 0.1000000 30  )=   6.128204                                   dl(    5.532636 0.1000000 30  )=   6.894230                                   dl(    6.032636 0.1000000 30  )=   7.660254                                   gama(beta = 0.1000000                                                                       alfa = 35) >   1.045747                                         gama        beta      alfa                                                    dl(    1.045747 0.1000000 35  )=   0.0000000E + 00                            dl(    1.545747 0.1000000 35  )=   0.6269017                                  dl(    2.045747 0.1000000 35  )=   1.253803                                   dl(    2.545747 0.1000000 35  )=   1.880705                                   dl(    3.045747 0.1000000 35  )=   2.507607                                   dl(    3.545747 0.1000000 35  )=   3.134508                                   dl(    4.045747 0.1000000 35  )=   3.761410                                   dl(    4.545747 0.1000000 35  )=   4.388311                                   dl(    5.045747 0.1000000 35  )=   5.015213                                   dl(    5.545747 0.1000000 35  )=   5.642115                                   dl(    6.045747 0.1000000 35  )=   6.269017                                   gama(beta = 0.1000000                                                                       alfa = 40) >   1.062034                                         gama        beta      alfa                                                    dl(    1.062034 0.1000000 40  )=  -7.1034052E - 08                            dl(    1.562034 0.1000000 40  )=    0.5180907                                 dl(    2.062034 0.1000000 40  )=    1.036181                                  dl(    2.562034 0.1000000 40  )=    1.554272                                  dl(    3.062034 0.1000000 40  )=    2.072362                                  dl(    3.562034 0.1000000 40  )=    2.590453                                  dl(    4.062034 0.1000000 40  )=    3.108544                                  dl(    4.562034 0.1000000 40  )=    3.626635                                  dl(    5.062034 0.1000000 40  )=    4.144725                                  dl(    5.562034 0.1000000 40  )=    4.662816                                  dl(    6.062034 0.1000000 40  )=    5.180906                                  gama(beta = 0.1000000                                                                       alfa = 45) >   1.082358                                         gama        beta      alfa                                                    dl(    1.082358 0.1000000 45  )=   0.0000000E + 00                            dl(    1.582358 0.1000000 45  )=   0.4292893                                  dl(    2.082358 0.1000000 45  )=   0.8585786                                  dl(    2.582358 0.1000000 45  )=   1.287868                                   dl(    3.082358 0.1000000 45  )=   1.717157                                   dl(    3.582358 0.1000000 45  )=   2.146446                                   dl(    4.082358 0.1000000 45  )=   2.575736                                   dl(    4.582358 0.1000000 45  )=   3.005025                                   dl(    5.082358 0.1000000 45  )=   3.434314                                   dl(    5.582358 0.1000000 45  )=   3.863604                                   dl(    6.082358 0.1000000 45  )=   4.292893                                   gama(beta = 0.1000000                                                                       alfa = 50) >   1.108113                                         gama        beta      alfa                                                    dl(    1.108113 0.1000000 50  )=   0.0000000E + 00                            dl(    1.608113 0.1000000 50  )=   0.3542794                                  dl(    2.108113 0.1000000 50  )=   0.7085589                                  dl(    2.608113 0.1000000 50  )=   1.062838                                   dl(    3.108113 0.1000000 50  )=   1.417118                                   dl(    3.608113 0.1000000 50  )=   1.771397                                   dl(    4.108113 0.1000000 50  )=   2.125677                                   dl(    4.608113 0.1000000 50  )=   2.479956                                   dl(    5.108113 0.1000000 50  )=   2.834235                                   dl(    5.608113 0.1000000 50  )=   3.188515                                   dl(    6.108113 0.1000000 50  )=   3.542794                                   gama(beta = 0.1000000                                                                       alfa = 55) >   1.141690                                         gama        beta      alfa                                                    dl(    1.141690 0.1000000 55  )=   0.0000000E + 00                            dl(    1.641690 0.1000000 55  )=   0.2890651                                  dl(    2.141690 0.1000000 55  )=   0.5781302                                  dl(    2.641690 0.1000000 55  )=   0.8671951                                  dl(    3.141690 0.1000000 55  )=   1.156260                                   dl(    3.641690 0.1000000 55  )=   1.445325                                   dl(    4.141690 0.1000000 55  )=   1.734390                                   dl(    4.641690 0.1000000 55  )=   2.023455                                   dl(    5.141690 0.1000000 55  )=   2.312521                                   dl(    5.641690 0.1000000 55  )=   2.601585                                   dl(    6.141690 0.1000000 55  )=   2.890651                                   gama(beta = 0.1000000                                                                       alfa = 60) >   1.187500                                         gama        beta      alfa                                                    dl(    1.187500 0.1000000 60  )=   0.0000000E + 00                            dl(    1.687500 0.1000000 60  )=   0.2309401                                  dl(    2.187500 0.1000000 60  )=   0.4618802                                  dl(    2.687500 0.1000000 60  )=   0.6928203                                  dl(    3.187500 0.1000000 60  )=   0.9237604                                  dl(    3.687500 0.1000000 60  )=   1.154701                                   dl(    4.187500 0.1000000 60  )=   1.385641                                   dl(    4.687500 0.1000000 60  )=   1.616581                                   dl(    5.187500 0.1000000 60  )=   1.847521                                   dl(    5.687500 0.1000000 60  )=   2.078461                                   dl(    6.187500 0.1000000 60  )=   2.309401                                   gama(beta = 0.1000000                                                                       alfa = 65) >   1.254602                                         gama        beta      alfa                                                    dl(    1.254602 0.1000000 65  )=   0.0000000E + 00                            dl(    1.754602 0.1000000 65  )=   0.1779849                                  dl(    2.254602 0.1000000 65  )=   0.3559698                                  dl(    2.754602 0.1000000 65  )=   0.5339549                                  dl(    3.254602 0.1000000 65  )=   0.7119397                                  dl(    3.754602 0.1000000 65  )=   0.8899247                                  dl(    4.254602 0.1000000 65  )=   1.067910                                   dl(    4.754602 0.1000000 65  )=   1.245895                                   dl(    5.254602 0.1000000 65  )=   1.423879                                   dl(    5.754602 0.1000000 65  )=   1.601864                                   dl(    6.254602 0.1000000 65  )=   1.779849                                   gama(beta = 0.1000000                                                                       alfa = 70) >   1.364855                                         gama        beta      alfa                                                    dl(    1.364855 0.1000000 70  )=   0.0000000E + 00                            dl(    1.864855 0.1000000 70  )=   0.1287762                                  dl(    2.364855 0.1000000 70  )=   0.2575525                                  dl(    2.864855 0.1000000 70  )=   0.3863288                                  dl(    3.364855 0.1000000 70  )=   0.5151050                                  dl(    3.864855 0.1000000 70  )=   0.6438813                                  dl(    4.364855 0.1000000 70  )=   0.7726575                                  dl(    4.864855 0.1000000 70  )=   0.9014338                                  dl(    5.364855 0.1000000 70  )=   1.030210                                   dl(    5.864855 0.1000000 70  )=   1.158986                                   dl(    6.364855 0.1000000 70  )=   1.287763                                   gama(beta = 0.1000000                                                                       alfa = 75) >   1.587469                                         gama        beta      alfa                                                    dl(    1.587469 0.1000000 75  )=   0.0000000E + 00                            dl(    2.087469 0.1000000 75  )=   8.2210816E - 02                            dl(    2.587469 0.1000000 75  )=   0.1644216                                  dl(    3.087469 0.1000000 75  )=   0.2466324                                  dl(    3.587469 0.1000000 75  )=   0.3288433                                  dl(    4.087469 0.1000000 75  )=   0.4110541                                  dl(    4.587469 0.1000000 75  )=   0.4932648                                  dl(    5.087469 0.1000000 75  )=   0.5754756                                  dl(    5.587469 0.1000000 75  )=   0.6576865                                  dl(    6.087469 0.1000000 75  )=   0.7398973                                  dl(    6.587469 0.1000000 75  )=   0.8221080                                  gama(beta = 0.1000000                                                                       alfa = 80) >   2.316863                                         gama        beta      alfa                                                    dl(    2.316863 0.1000000 80  )=  -1.0509909E - 08                            dl(    2.816863 0.1000000 80  )=    3.7392177E - 02                           dl(    3.316863 0.1000000 80  )=    7.4784376E - 02                           dl(    3.816863 0.1000000 80  )=    0.1121766                                 dl(    4.316863 0.1000000 80  )=    0.1495687                                 dl(    4.816863 0.1000000 80  )=    0.1869609                                 dl(    5.316863 0.1000000 80  )=    0.2243531                                 dl(    5.816863 0.1000000 80  )=    0.2617453                                 dl(    6.316863 0.1000000 80  )=    0.2991375                                 dl(    6.816863 0.1000000 80  )=    0.3365296                                 dl(    7.316863 0.1000000 80  )=    0.3739218                                 gama(beta = 0.2000000                                                                       alfa =  5) >   1.001908                                         gama        beta      alfa                                                    dl(    1.001908 0.2000000  5  )=   0.0000000E + 00                            dl(    1.501908 0.2000000  5  )=   4.567655                                   dl(    2.001908 0.2000000  5  )=   9.135310                                   dl(    2.501908 0.2000000  5  )=  13.70297                                    dl(    3.001908 0.2000000  5  )=  18.27062                                    dl(    3.501908 0.2000000  5  )=  22.83828                                    dl(    4.001908 0.2000000  5  )=  27.40593                                    dl(    4.501908 0.2000000  5  )=  31.97359                                    dl(    5.001908 0.2000000  5  )=  36.54124                                    dl(    5.501908 0.2000000  5  )=  41.10890                                    dl(    6.001908 0.2000000  5  )=  45.67656                                    gama(beta = 0.2000000                                                                       alfa = 10) >   1.007684                                         gama        beta      alfa                                                    dl(    1.007684 0.2000000 10  )=   0.0000000E + 00                            dl(    1.507684 0.2000000 10  )=   2.259764                                   dl(    2.007684 0.2000000 10  )=   4.519529                                   dl(    2.507684 0.2000000 10  )=   6.779292                                   dl(    3.007684 0.2000000 10  )=   9.039058                                   dl(    3.507684 0.2000000 10  )=  11.29882                                    dl(    4.007684 0.2000000 10  )=  13.55858                                    dl(    4.507684 0.2000000 10  )=  15.81835                                    dl(    5.007684 0.2000000 10  )=  18.07811                                    dl(    5.507684 0.2000000 10  )=  20.33787                                    dl(    6.007684 0.2000000 10  )=  22.59764                                    gama(beta = 0.2000000                                                                       alfa = 15) >   1.017492                                         gama        beta      alfa                                                    dl(    1.017492 0.2000000 15  )=   0.0000000E + 00                            dl(    1.517492 0.2000000 15  )=   1.479655                                   dl(    2.017492 0.2000000 15  )=   2.959310                                   dl(    2.517492 0.2000000 15  )=   4.438965                                   dl(    3.017492 0.2000000 15  )=   5.918621                                   dl(    3.517492 0.2000000 15  )=   7.398275                                   dl(    4.017492 0.2000000 15  )=   8.877931                                   dl(    4.517492 0.2000000 15  )=  10.35759                                    dl(    5.017492 0.2000000 15  )=  11.83724                                    dl(    5.517492 0.2000000 15  )=  13.31690                                    dl(    6.017492 0.2000000 15  )=  14.79655                                    gama(beta = 0.2000000                                                                       alfa = 20) >   1.031629                                         gama        beta      alfa                                                    dl(    1.031629 0.2000000 20  )=   0.0000000E + 00                            dl(    1.531629 0.2000000 20  )=   1.081358                                   dl(    2.031629 0.2000000 20  )=   2.162717                                   dl(    2.531629 0.2000000 20  )=   3.244075                                   dl(    3.031629 0.2000000 20  )=   4.325433                                   dl(    3.531629 0.2000000 20  )=   5.406792                                   dl(    4.031629 0.2000000 20  )=   6.488149                                   dl(    4.531629 0.2000000 20  )=   7.569508                                   dl(    5.031629 0.2000000 20  )=   8.650867                                   dl(    5.531629 0.2000000 20  )=   9.732225                                   dl(    6.031629 0.2000000 20  )=  10.81358                                    gama(beta = 0.2000000                                                                       alfa = 25) >   1.050575                                         gama        beta      alfa                                                    dl(    1.050575 0.2000000 25  )=   0.0000000E + 00                            dl(    1.550575 0.2000000 25  )=   0.8356334                                  dl(    2.050575 0.2000000 25  )=   1.671267                                   dl(    2.550575 0.2000000 25  )=   2.506900                                   dl(    3.050575 0.2000000 25  )=   3.342533                                   dl(    3.550575 0.2000000 25  )=   4.178166                                   dl(    4.050575 0.2000000 25  )=   5.013800                                   dl(    4.550575 0.2000000 25  )=   5.849433                                   dl(    5.050575 0.2000000 25  )=   6.685066                                   dl(    5.550575 0.2000000 25  )=   7.520700                                   dl(    6.050575 0.2000000 25  )=   8.356333                                   gama(beta = 0.2000000                                                                       alfa = 30) >   1.075072                                         gama        beta      alfa                                                    dl(    1.075072 0.2000000 30  )=  -1.0323828E - 07                            dl(    1.575072 0.2000000 30  )=    0.6660254                                 dl(    2.075072 0.2000000 30  )=    1.332051                                  dl(    2.575072 0.2000000 30  )=    1.998076                                  dl(    3.075072 0.2000000 30  )=    2.664102                                  dl(    3.575072 0.2000000 30  )=    3.330127                                  dl(    4.075072 0.2000000 30  )=    3.996153                                  dl(    4.575072 0.2000000 30  )=    4.662178                                  dl(    5.075072 0.2000000 30  )=    5.328203                                  dl(    5.575072 0.2000000 30  )=    5.994229                                  dl(    6.075072 0.2000000 30  )=    6.660254                                  gama(beta = 0.2000000                                                                       alfa = 35) >   1.106271                                         gama        beta      alfa                                                    dl(    1.106271 0.2000000 35  )=   0.0000000E + 00                            dl(    1.606271 0.2000000 35  )=   0.5397293                                  dl(    2.106271 0.2000000 35  )=   1.079459                                   dl(    2.606271 0.2000000 35  )=   1.619188                                   dl(    3.106271 0.2000000 35  )=   2.158918                                   dl(    3.606271 0.2000000 35  )=   2.698647                                   dl(    4.106271 0.2000000 35  )=   3.238376                                   dl(    4.606271 0.2000000 35  )=   3.778105                                   dl(    5.106271 0.2000000 35  )=   4.317834                                   dl(    5.606271 0.2000000 35  )=   4.857564                                   dl(    6.106271 0.2000000 35  )=   5.397293                                   gama(beta = 0.2000000                                                                       alfa = 40) >   1.145987                                         gama        beta      alfa                                                    dl(    1.145987 0.2000000 40  )=   0.0000000E + 00                            dl(    1.645987 0.2000000 40  )=   0.4403043                                  dl(    2.145987 0.2000000 40  )=   0.8806087                                  dl(    2.645987 0.2000000 40  )=   1.320913                                   dl(    3.145987 0.2000000 40  )=   1.761218                                   dl(    3.645987 0.2000000 40  )=   2.201522                                   dl(    4.145987 0.2000000 40  )=   2.641827                                   dl(    4.645987 0.2000000 40  )=   3.082131                                   dl(    5.145987 0.2000000 40  )=   3.522435                                   dl(    5.645987 0.2000000 40  )=   3.962740                                   dl(    6.145987 0.2000000 40  )=   4.403044                                   gama(beta = 0.2000000                                                                       alfa = 45) >   1.197197                                         gama        beta      alfa                                                    dl(    1.197197 0.2000000 45  )=   0.0000000E + 00                            dl(    1.697197 0.2000000 45  )=   0.3585786                                  dl(    2.197197 0.2000000 45  )=   0.7171574                                  dl(    2.697197 0.2000000 45  )=   1.075736                                   dl(    3.197197 0.2000000 45  )=   1.434315                                   dl(    3.697197 0.2000000 45  )=   1.792893                                   dl(    4.197197 0.2000000 45  )=   2.151472                                   dl(    4.697197 0.2000000 45  )=   2.510051                                   dl(    5.197197 0.2000000 45  )=   2.868629                                   dl(    5.697197 0.2000000 45  )=   3.227208                                   dl(    6.197197 0.2000000 45  )=   3.585786                                   gama(beta = 0.2000000                                                                       alfa = 50) >   1.265059                                         gama        beta      alfa                                                    dl(    1.265059 0.2000000 50  )=   0.0000000E + 00                            dl(    1.765059 0.2000000 50  )=   0.2890092                                  dl(    2.265059 0.2000000 50  )=   0.5780182                                  dl(    2.765059 0.2000000 50  )=   0.8670272                                  dl(    3.265059 0.2000000 50  )=   1.156036                                   dl(    3.765059 0.2000000 50  )=   1.445045                                   dl(    4.265059 0.2000000 50  )=   1.734055                                   dl(    4.765059 0.2000000 50  )=   2.023064                                   dl(    5.265059 0.2000000 50  )=   2.312073                                   dl(    5.765059 0.2000000 50  )=   2.601082                                   dl(    6.265059 0.2000000 50  )=   2.890091                                   gama(beta = 0.2000000                                                                       alfa = 55) >   1.359236                                         gama        beta      alfa                                                    dl(    1.359236 0.2000000 55  )=   0.0000000E + 00                            dl(    1.859236 0.2000000 55  )=   0.2280263                                  dl(    2.359236 0.2000000 55  )=   0.4560528                                  dl(    2.859236 0.2000000 55  )=   0.6840791                                  dl(    3.359236 0.2000000 55  )=   0.9121054                                  dl(    3.859236 0.2000000 55  )=   1.140132                                   dl(    4.359236 0.2000000 55  )=   1.368158                                   dl(    4.859236 0.2000000 55  )=   1.596184                                   dl(    5.359236 0.2000000 55  )=   1.824211                                   dl(    5.859236 0.2000000 55  )=   2.052237                                   dl(    6.359236 0.2000000 55  )=   2.280263                                   gama(beta = 0.2000000                                                                       alfa = 60) >   1.500000                                         gama        beta      alfa                                                    dl(    1.500000 0.2000000  5  )=   0.0000000E + 00                            dl(    2.000000 0.2000000 60  )=   0.1732051                                  dl(    2.500000 0.2000000 60  )=   0.3464102                                  dl(    3.000000 0.2000000 60  )=   0.5196153                                  dl(    3.500000 0.2000000 60  )=   0.6928202                                  dl(    4.000000 0.2000000 60  )=   0.8660252                                  dl(    4.500000 0.2000000 60  )=   1.039230                                   dl(    5.000000 0.2000000 60  )=   1.212435                                   dl(    5.500000 0.2000000 60  )=   1.385640                                   dl(    6.000000 0.2000000 60  )=   1.558846                                   dl(    6.500000 0.2000000 60  )=   1.732051                                   gama(beta = 0.2000000                                                                       alfa = 65) >   1.737939                                         gama        beta      alfa                                                    dl(    1.000848 0.2000000 65  )=   0.0000000E + 00                            dl(    2.237939 0.2000000 65  )=   0.1228161                                  dl(    2.737939 0.2000000 65  )=   0.2456321                                  dl(    3.237939 0.2000000 65  )=   0.3684481                                  dl(    3.737939 0.2000000 65  )=   0.4912642                                  dl(    4.237939 0.2000000 65  )=   0.6140803                                  dl(    4.737939 0.2000000 65  )=   0.7368963                                  dl(    5.237939 0.2000000 65  )=   0.8597122                                  dl(    5.737939 0.2000000 65  )=   0.9825283                                  dl(    6.237939 0.2000000 65  )=   1.105344                                   dl(    6.737939 0.2000000 65  )=   1.228161                                   gama(beta = 0.2000000                                                                       alfa = 70) >   2.243517                                         gama        beta      alfa                                                    dl(    2.243517 0.2000000 70  )=   0.0000000E + 00                            dl(    2.743517 0.2000000 70  )=   7.5567380E - 02                            dl(    3.243517 0.2000000 70  )=   0.1511347                                  dl(    3.743517 0.2000000 70  )=   0.2267021                                  dl(    4.243517 0.2000000 70  )=   0.3022694                                  dl(    4.743517 0.2000000 70  )=   0.3778368                                  dl(    5.243517 0.2000000 70  )=   0.4534041                                  dl(    5.743517 0.2000000 70  )=   0.5289715                                  dl(    6.243517 0.2000000 70  )=   0.6045388                                  dl(    6.743517 0.2000000 70  )=   0.6801062                                  dl(    7.243517 0.2000000 70  )=   0.7556735                                  gama(beta = 0.2000000                                                                       alfa = 75) >   4.172484                                         gama        beta      alfa                                                    dl(    4.172484 0.2000000 75  )=   0.0000000E + 00                            dl(    4.672484 0.2000000 75  )=   3.0446989E - 02                            dl(    5.172484 0.2000000 75  )=   6.0893979E - 02                            dl(    5.672484 0.2000000 75  )=   9.1340967E - 02                            dl(    6.172484 0.2000000 75  )=   0.1217880                                  dl(    6.672484 0.2000000 75  )=   0.1522349                                  dl(    7.172484 0.2000000 75  )=   0.1826819                                  dl(    7.672484 0.2000000 75  )=   0.2131289                                  dl(    8.172484 0.2000000 75  )=   0.2435759                                  dl(    8.672484 0.2000000 75  )=   0.2740229                                  dl(    9.172484 0.2000000 75  )=   0.3044699                                  gama(beta = 0.3000000                                                                       alfa =  5) >   1.003273                                         gama        beta      alfa                                                    dl(    1.003273 0.3000000  5  )=   0.0000000E + 00                            dl(    1.503273 0.3000000  5  )=   3.993970                                   dl(    2.003273 0.3000000  5  )=   7.987939                                   dl(    2.503273 0.3000000  5  )=  11.98191                                    dl(    3.003273 0.3000000  5  )=  15.97588                                    dl(    3.503273 0.3000000  5  )=  19.96985                                    dl(    4.003273 0.3000000  5  )=  23.96382                                    dl(    4.503273 0.3000000  5  )=  27.95779                                    dl(    5.003273 0.3000000  5  )=  31.95176                                    dl(    5.503273 0.3000000  5  )=  35.94573                                    dl(    6.003273 0.3000000  5  )=  39.93970                                    gama(beta = 0.3000000                                                                       alfa = 10) >   1.013210                                         gama        beta      alfa                                                    dl(    1.013210 0.3000000 10  )=   0.0000000E + 00                            dl(    1.513210 0.3000000 10  )=   1.971826                                   dl(    2.013210 0.3000000 10  )=   3.943652                                   dl(    2.513210 0.3000000 10  )=   5.915477                                   dl(    3.013210 0.3000000 10  )=   7.887302                                   dl(    3.513210 0.3000000 10  )=   9.859128                                   dl(    4.013210 0.3000000 10  )=  11.83095                                    dl(    4.513210 0.3000000 10  )=  13.80278                                    dl(    5.013210 0.3000000 10  )=  15.77460                                    dl(    5.513210 0.3000000 10  )=  17.74643                                    dl(    6.013210 0.3000000 10  )=  19.71825                                    gama(beta = 0.3000000                                                                       alfa = 15) >   1.030178                                         gama        beta      alfa                                                    dl(    1.030178 0.3000000 15  )=   0.0000000E + 00                            dl(    1.530178 0.3000000 15  )=   1.286470                                   dl(    2.030178 0.3000000 15  )=   2.572940                                   dl(    2.530178 0.3000000 15  )=   3.859410                                   dl(    3.030178 0.3000000 15  )=   5.145880                                   dl(    3.530178 0.3000000 15  )=   6.432350                                   dl(    4.030178 0.3000000 15  )=   7.718821                                   dl(    4.530178 0.3000000 15  )=   9.005290                                   dl(    5.030178 0.3000000 15  )=  10.29176                                    dl(    5.530178 0.3000000 15  )=  11.57823                                    dl(    6.030178 0.3000000 15  )=  12.86470                                    gama(beta = 0.3000000                                                                       alfa = 20) >   1.054860                                         gama        beta      alfa                                                    dl(    1.054860 0.3000000 20  )=   0.0000000E + 00                            dl(    1.554860 0.3000000 20  )=   0.9351683                                  dl(    2.054860 0.3000000 20  )=   1.870337                                   dl(    2.554860 0.3000000 20  )=   2.805505                                   dl(    3.054860 0.3000000 20  )=   3.740673                                   dl(    3.554860 0.3000000 20  )=   4.675841                                   dl(    4.054860 0.3000000 20  )=   5.611008                                   dl(    4.554860 0.3000000 20  )=   6.546177                                   dl(    5.054860 0.3000000 20  )=   7.481345                                   dl(    5.554860 0.3000000 20  )=   8.416512                                   dl(    6.054860 0.3000000 20  )=   9.351681                                   gama(beta = 0.3000000                                                                       alfa = 25) >   1.088374                                         gama        beta      alfa                                                    dl(    1.088374 0.3000000 25  )=   0.0000000E + 00                            dl(    1.588374 0.3000000 25  )=   0.7173234                                  dl(    2.088374 0.3000000 25  )=   1.434647                                   dl(    2.588374 0.3000000 25  )=   2.151970                                   dl(    3.088374 0.3000000 25  )=   2.869293                                   dl(    3.588374 0.3000000 25  )=   3.586617                                   dl(    4.088374 0.3000000 25  )=   4.303940                                   dl(    4.588374 0.3000000 25  )=   5.021263                                   dl(    5.088374 0.3000000 25  )=   5.738586                                   dl(    5.588374 0.3000000 25  )=   6.455910                                   dl(    6.088374 0.3000000 25  )=   7.173233                                   gama(beta = 0.3000000                                                                       alfa = 30) >   1.132503                                         gama        beta      alfa                                                    dl(    1.132503 0.3000000 30  )=   0.0000000E + 00                            dl(    1.632503 0.3000000 30  )=   0.5660253                                  dl(    2.132503 0.3000000 30  )=   1.132051                                   dl(    2.632503 0.3000000 30  )=   1.698076                                   dl(    3.132503 0.3000000 30  )=   2.264102                                   dl(    3.632503 0.3000000 30  )=   2.830127                                   dl(    4.132503 0.3000000 30  )=   3.396153                                   dl(    4.632503 0.3000000 30  )=   3.962178                                   dl(    5.132503 0.3000000 30  )=   4.528203                                   dl(    5.632503 0.3000000 30  )=   5.094229                                   dl(    6.132503 0.3000000 30  )=   5.660254                                   gama(beta = 0.3000000                                                                       alfa = 35) >   1.190112                                         gama        beta      alfa                                                    dl(    1.190112 0.3000000 35  )=   0.0000000E + 00                            dl(    1.690112 0.3000000 35  )=   0.4525571                                  dl(    2.190112 0.3000000 35  )=   0.9051141                                  dl(    2.690112 0.3000000 35  )=   1.357671                                   dl(    3.190112 0.3000000 35  )=   1.810228                                   dl(    3.690112 0.3000000 35  )=   2.262785                                   dl(    4.190112 0.3000000 35  )=   2.715343                                   dl(    4.690112 0.3000000 35  )=   3.167900                                   dl(    5.190112 0.3000000 35  )=   3.620456                                   dl(    5.690112 0.3000000 35  )=   4.073013                                   dl(    6.190112 0.3000000 35  )=   4.525570                                   gama(beta = 0.3000000                                                                       alfa = 40) >   1.265968                                         gama        beta      alfa                                                    dl(    1.265968 0.3000000 40  )=   0.0000000E + 00                            dl(    1.765968 0.3000000 40  )=   0.3625183                                  dl(    2.265968 0.3000000 40  )=   0.7250366                                  dl(    2.765968 0.3000000 40  )=   1.087555                                   dl(    3.265968 0.3000000 40  )=   1.450073                                   dl(    3.765968 0.3000000 40  )=   1.812591                                   dl(    4.265968 0.3000000 40  )=   2.175110                                   dl(    4.765968 0.3000000 40  )=   2.537628                                   dl(    5.265968 0.3000000 40  )=   2.900146                                   dl(    5.765968 0.3000000 40  )=   3.262665                                   dl(    6.265968 0.3000000 40  )=   3.625183                                   gama(beta = 0.3000000                                                                       alfa = 45) >   1.368454                                         gama        beta      alfa                                                    dl(    1.368454 0.3000000  5  )=   0.0000000E + 00                            dl(    1.868454 0.3000000 45  )=   0.2878680                                  dl(    2.368454 0.3000000 45  )=   0.5757360                                  dl(    2.868454 0.3000000 45  )=   0.8636041                                  dl(    3.368454 0.3000000 45  )=   1.151472                                   dl(    3.868454 0.3000000 45  )=   1.439340                                   dl(    4.368454 0.3000000 45  )=   1.727208                                   dl(    4.868454 0.3000000 45  )=   2.015076                                   dl(    5.368454 0.3000000 45  )=   2.302944                                   dl(    5.868454 0.3000000 45  )=   2.590812                                   dl(    6.368454 0.3000000 45  )=   2.878680                                   gama(beta = 0.3000000                                                                       alfa = 50) >   1.513575                                         gama        beta      alfa                                                    dl(    1.513575 0.3000000 50  )=   0.0000000E + 00                            dl(    2.013575 0.3000000 50  )=   0.2237388                                  dl(    2.513575 0.3000000 50  )=   0.4474775                                  dl(    3.013575 0.3000000 50  )=   0.6712162                                  dl(    3.513575 0.3000000 50  )=   0.8949549                                  dl(    4.013576 0.3000000 50  )=   1.118694                                   dl(    4.513576 0.3000000 50  )=   1.342432                                   dl(    5.013576 0.3000000 50  )=   1.566171                                   dl(    5.513576 0.3000000 50  )=   1.789910                                   dl(    6.013576 0.3000000 50  )=   2.013649                                   dl(    6.513576 0.3000000 50  )=   2.237387                                   gama(beta = 0.3000000                                                                       alfa = 55) >   1.735820                                         gama        beta      alfa                                                    dl(    1.735820 0.3000000 55  )=   0.0000000E + 00                            dl(    2.235820 0.3000000 55  )=   0.1669876                                  dl(    2.735820 0.3000000 55  )=   0.3339752                                  dl(    3.235820 0.3000000 55  )=   0.5009628                                  dl(    3.735820 0.3000000 55  )=   0.6679505                                  dl(    4.235820 0.3000000 55  )=   0.8349380                                  dl(    4.735820 0.3000000 55  )=   1.001926                                   dl(    5.235820 0.3000000 55  )=   1.168913                                   dl(    5.735820 0.3000000 55  )=   1.335901                                   dl(    6.235820 0.3000000 55  )=   1.502888                                   dl(    6.735820 0.3000000 55  )=   1.669876                                   gama(beta = 0.3000000                                                                       alfa = 60) >   2.125000                                         gama        beta      alfa                                                    dl(    2.125000 0.3000000 60  )=   0.0000000E + 00                            dl(    2.625000 0.3000000 60  )=   0.1154701                                  d1)    3.125000 0.3000000 60  )=   0.2309401                                  dl(    3.625000 0.3000000 60  )=   0.3464102                                  dl(    4.125000 0.3000000 60  )=   0.4618802                                  dl(    4.625000 0.3000000 60  )=   0.5773503                                  dl(    5.125000 0.3000000 60  )=   0.6928203                                  dl(    5.625000 0.3000000 60  )=   0.8082904                                  dl(    6.125000 0.3000000 60  )=   0.9237605                                  dl(    6.625000 0.3000000 60  )=   1.039231                                   dl(    7.125000 0.3000000 60  )=   1.154701                                   gama(beta = 0.3000000                                                                       alfa = 65) >   3.009636                                         gama        beta      alfa                                                    dl(    3.009636 0.3000000 65  )=   0.0000000E + 00                            dl(    3.509636 0.3000000 65  )=   6.7647174E - 02                            dl(    4.009636 0.3000000 65  )=   0.1352943                                  dl(    4.509636 0.3000000 65  )=   0.2029415                                  dl(    5.009636 0.3000000 65  )=   0.2705886                                  dl(    5.509636 0.3000000 65  )=   0.3382358                                  dl(    6.009636 0.3000000 65  )=   0.4058830                                  dl(    6.509636 0.3000000 65  )=   0.4735300                                  dl(    7.009636 0.3000000 65  )=   0.5411772                                  dl(    7.509636 0.3000000 65  )=   0.6088244                                  dl(    8.009637 0.3000000 65  )=   0.6764715                                  gama(beta = 0.3000000                                                                       alfa = 70) >   7.304273                                         gama        beta      alfa                                                    dl(    7.304273 0.3000000 70  )=   0.0000000E + 00                            dl(    7.804273 0.3000000 70  )=   2.2358468E - 02                            dl(    8.304274 0.3000000 70  )=   4.4716977E - 02                            dl(    8.804274 0.3000000 70  )=   6.7075446E - 02                            dl(    9.304274 0.3000000 70  )=   8.9433916E - 02                            dl(    9.804274 0.3000000 70  )=   0.1117924                                  dl(   10.30427  0.3000000 70  )=   0.1341508                                  dl(   10.80427  0.3000000 70  )=   0.1565093                                  dl(   11.30427  0.3000000 70  )=   0.1788678                                  dl(   11.80427  0.3000000 70  )=   0.2012262                                  dl(   12.30427  0.3000000 70  )=   0.2235847                                  gama(beta = 0.4000000                                                                       alfa =  5) >   1.005096                                         gama        beta      alfa                                                    dl(    1.005096 0.4000000  5  )=   0.0000000E + 00                            dl(    1.505096 0.4000000  5  )=   3.420284                                   dl(    2.005096 0.4000000  5  )=   6.840568                                   dl(    2.505096 0.4000000  5  )=  10.26085                                    dl(    3.005096 0.4000000  5  )=  13.68113                                    dl(    3.505096 0.4000000  5  )=  17.10142                                    dl(    4.005096 0.4000000  5  )=  20.52170                                    dl(    4.505096 0.4000000  5  )=  23.94199                                    dl(    5.005096 0.4000000  5  )=  27.36227                                    dl(    5.505096 0.4000000  5  )=  30.78255                                    dl(    6.005096 0.4000000  5  )=  34.20284                                    gama(beta = 0.4000000                                                                       alfa = 10) >   1.020625                                         gama        beta      alfa                                                    dl(    1.020625 0.4000000 10  )=   0.0000000E + 00                            dl(    1.520625 0.4000000 10  )=   1.683887                                   dl(    2.020625 0.4000000 10  )=   3.367775                                   dl(    2.520625 0.4000000 10  )=   5.051661                                   dl(    3.020625 0.4000000 10  )=   6.735548                                   dl(    3.520625 0.4000000 10  )=   8.419435                                   dl(    4.020625 0.4000000 10  )=  10.10332                                    dl(    4.520625 0.4000000 10  )=  11.78721                                    dl(    5.020625 0.4000000 10  )=  13.47109                                    dl(    5.520625 0.4000000 10  )=  15.15498                                    dl(    6.020625 0.4000000 10  )=  16.83887                                    gama(beta = 0.4000000                                                                       alfa = 15) >   1.047347                                         gama        beta      alfa                                                    dl(    1.047347 0.4000000 15  )=   0.0000000E + 00                            dl(    1.547347 0.4000000 15  )=   1.093285                                   dl(    2.047347 0.4000000 15  )=   2.186569                                   dl(    2.547347 0.4000000 15  )=   3.279854                                   dl(    3.047347 0.4000000 15  )=   4.373139                                   dl(    3.547347 0.4000000 15  )=   5.466424                                   dl(    4.047347 0.4000000 15  )=   6.559709                                   dl(    4.547347 0.4000000 15  )=   7.652993                                   dl(    5.047347 0.4000000 15  )=   8.746278                                   dl(    5.547347 0.4000000 15  )=   9.839563                                   dl(    6.047347 0.4000000 15  )=  10.93285                                    gama(beta = 0.4000000                                                                       alfa = 20) >   1.086700                                         gama        beta      alfa                                                    dl(    1.086700 0.4000000 20  )=   0.0000000E + 00                            dl(    1.586700 0.4000000 20  )=   0.7889779                                  dl(    2.086700 0.4000000 20  )=   1.577956                                   dl(    2.586700 0.4000000 20  )=   2.366934                                   dl(    3.086700 0.4000000 20  )=   3.155912                                   dl(    3.586700 0.4000000 20  )=   3.944890                                   dl(    4.086699 0.4000000 20  )=   4.733867                                   dl(    4.586699 0.4000000 20  )=   5.522845                                   dl(    5.086699 0.4000000 20  )=   6.311823                                   dl(    5.586699 0.4000000 20  )=   7.100801                                   dl(    6.086699 0.4000000 20  )=   7.889779                                   gama(beta = 0.4000000                                                                       alfa = 25) >   1.141105                                         gama        beta      alfa                                                    dl(    1.141105 0.4000000 25  )=   0.0000000E + 00                            dl(    1.641105 0.4000000 25  )=   0.5990134                                  dl(    2.141105 0.4000000 25  )=   1.198027                                   dl(    2.641105 0.4000000 25  )=   1.797040                                   dl(    3.141105 0.4000000 25  )=   2.396053                                   dl(    3.641105 0.4000000 25  )=   2.995066                                   dl(    4.141105 0.4000000 25  )=   3.594079                                   dl(    4.641105 0.4000000 25  )=   4.193092                                   dl(    5.141105 0.4000000 25  )=   4.792106                                   dl(    5.641105 0.4000000 25  )=   5.391119                                   dl(    6.141105 0.4000000 25  )=   5.990132                                   gama(beta = 0.4000000                                                                       alfa = 30) >   1.214581                                         gama        beta      alfa                                                    dl(    1.214581 0.4000000 30  )=   0.0000000E + 00                            dl(    1.714581 0.4000000 30  )=   0.4660254                                  dl(    2.214581 0.4000000 30  )=   0.9320508                                  dl(    2.714581 0.4000000 30  )=   1.398076                                   dl(    3.214581 0.4000000 30  )=   1.864102                                   dl(    3.714581 0.4000000 30  )=   2.330127                                   dl(    4.214581 0.4000000 30  )=   2.796153                                   dl(    4.714581 0.4000000 30  )=   3.262178                                   dl(    5.214581 0.4000000 30  )=   3.728203                                   dl(    5.714581 0.4000000 30  )=   4.194229                                   dl(    6.214581 0.4000000 30  )=   4.660254                                   gama(beta = 0.4000000                                                                       alfa = 35) >   1.313958                                         gama        beta      alfa                                                    dl(    1.313958 0.4000000 35  )=   0.0000000E + 00                            dl(    1.813958 0.4000000 35  )=   0.3653848                                  dl(    2.313958 0.4000000 35  )=   0.7307695                                  dl(    2.813958 0.4000000 35  )=   1.096154                                   dl(    3.313958 0.4000000 35  )=   1.461539                                   dl(    3.813958 0.4000000 35  )=   1.826923                                   dl(    4.313958 0.4000000 35  )=   2.192308                                   dl(    4.813958 0.4000000 35  )=   2.557693                                   dl(    5.313958 0.4000000 35  )=   2.923077                                   dl(    5.813958 0.4000000 35  )=   3.288462                                   dl(    6.313958 0.4000000 35  )=   3.653847                                   gama(beta = 0.4000000                                                                       alfa = 40 >    1.451504                                         gama        beta      alfa                                                    dl(    1.451504 0.4000000 40  )=   0.0000000E + 00                            dl(    1.951504 0.4000000 40  )=   0.2847320                                  dl(    2.451504 0.4000000 40  )=   0.5694641                                  dl(    2.951504 0.4000000 40  )=   0.8541961                                  dl(    3.451504 0.4000000 40  )=   1.138928                                   dl(    3.951504 0.4000000 40  )=   1.423660                                   dl(    4.451504 0.4000000 40  )=   1.708392                                   dl(    4.951504 0.4000000 40  )=   1.993124                                   dl(    5.451504 0.4000000 40  )=   2.277856                                   dl(    5.951504 0.4000000 40  )=   2.562588                                   dl(    6.451504 0.4000000 40  )=   2.847321                                   gama(beta = 0.4000000                                                                       alfa = 45) >   1.651239                                         gama        beta      alfa                                                    dl(    1.651239 0.4000000 45  )=   0.0000000E + 00                            dl(    2.151239 0.4000000 45  )=   0.2171572                                  dl(    2.651239 0.4000000 45  )=   0.4343146                                  dl(    3.151239 0.4000000 45  )=   0.6514719                                  dl(    3.651239 0.4000000 45  )=   0.8686291                                  dl(    4.151239 0.4000000 45  )=   1.085786                                   dl(    4.651239 0.4000000 45  )=   1.302943                                   dl(    5.151239 0.4000000 45  )=   1.520101                                   dl(    5.651239 0.4000000 45  )=   1.737258                                   dl(    6.151239 0.4000000 45  )=   1.954415                                   dl(    6.651239 0.4000000 45  )=   2.171573                                   gama(beta = 0.4000000                                                                       alfa = 50) >   1.966811                                         gama        beta      alfa                                                    dl(    1.966811 0.4000000 50  )=   0.0000000E + 00                            dl(    2.466811 0.4000000 50  )=   0.1584684                                  dl(    2.966811 0.4000000 50  )=   0.3169367                                  dl(    3.466811 0.4000000 50  )=   0.4754050                                  dl(    3.966811 0.4000000 50  )=   0.6338733                                  dl(    4.466811 0.4000000 50  )=   0.7923417                                  dl(    4.966811 0.4000000 50  )=   0.9508100                                  dl(    5.466811 0.4000000 50  )=   1.109279                                   dl(    5.966811 0.4000000 50  )=   1.267747                                   dl(    6.466811 0.4000000 50  )=   1.426215                                   dl(    6.966811 0.4000000 50  )=   1.584683                                   gama(beta = 0.4000000                                                                       alfa = 55) >   2.546316                                         gama        beta      alfa                                                    dl(    2.546316 0.4000000 55  )=   0.0000000E + 00                            dl(    3.046316 0.4000000 55  )=   0.1059489                                  dl(    3.546316 0.4000000 55  )=   0.2118977                                  dl(    4.046316 0.4000000 55  )=   0.3178467                                  dl(    4.546316 0.4000000 55  )=   0.4237956                                  dl(    5.046316 0.4000000 55  )=   0.5297443                                  dl(    5.546316 0.4000000 55  )=   0.6356933                                  dl(    6.046316 0.4000000 55  )=   0.7416422                                  dl(    6.546316 0.4000000 55  )=   0.8475911                                  dl(    7.046316 0.4000000 55  )=   0.9535400                                  dl(    7.546316 0.4000000 55  )=   1.059489                                   gama(beta = 0.4000000                                                                       alfa = 60) >   4.000001                                         gama        beta      alfa                                                    dl(    1.000848 0.4000000  5  )=   0.0000000E + 00                            dl(    4.500001 0.4000000 60  )=   5.7735037E - 02                            dl(    5.000001 0.4000000 60  )=   0.1154700                                  dl(    5.500001 0.4000000 60  )=   0.1732050                                  dl(    6.000001 0.4000000 60  )=   0.2309400                                  dl(    6.500001 0.4000000 60  )=   0.2886750                                  dl(    7.000001 0.4000000 60  )=   0.3464100                                  dl(    7.500001 0.4000000 60  )=   0.4041451                                  dl(    8.000002 0.4000000 60  )=   0.4618801                                  dl(    8.500002 0.4000000 60  )=   0.5196151                                  dl(    9.000002 0.4000000 60  )=   0.5773501                                  gama(beta = 0.4000000                                                                       alfa = 65) >   15.52622                                         gama        beta      alfa                                                    dl(   15.52622  0.4000000 65  )=   0.0000000E + 00                            dl(   16.02622  0.4000000 65  )=   1.2478273E - 02                            dl(   16.52622  0.4000000 65  )=   2.4956491E - 02                            dl(   17.02622  0.4000000 65  )=   3.7434764E - 02                            dl(   17.52622  0.4000000 65  )=   4.9912982E - 02                            dl(   18.02622  0.4000000 65  )=   6.2391199E - 02                            dl(   18.52622  0.4000000 65  )=   7.4869417E - 02                            dl(   19.02622  0.4000000 65  )=   8.7347694E - 02                            dl(   19.52622  0.4000000 65  )=   9.9825911E - 02                            dl(   20.02622  0.4000000 65  )=   0.1123041                                  dl(   20.52622  0.4000000 65  )=   0.1247824                                  gama(beta = 0.5000000                                                                       alfa =  5) >   1.007654                                         gama        beta      alfa                                                    dl(    1.007654 0.5000000  5  )=   0.0000000E + 00                            dl(    1.507654 0.5000000  5  )=   2.846598                                   dl(    2.007654 0.5000000  5  )=   5.693197                                   dl(    2.507654 0.5000000  5  )=   8.539796                                   dl(    3.007654 0.5000000  5  )=  11.38639                                    dl(    3.507654 0.5000000  5  )=  14.23299                                    dl(    4.007654 0.5000000  5  )=  17.07959                                    dl(    4.507654 0.5000000  5  )=  19.92619                                    dl(    5.007654 0.5000000  5  )=  22.77279                                    dl(    5.507654 0.5000000  5  )=  25.61938                                    dl(    6.007654 0.5000000  5  )=  28.46598                                    gama(beta = 0.5000000                                                                       alfa = 10) >   1.031099                                         gama        beta      alfa                                                    dl(    1.031099 0.5000000  5  )=   0.0000000E + 00                            dl(    1.531099 0.5000000 10  )=   1.395948                                   dl(    2.031099 0.5000000 10  )=   2.791897                                   dl(    2.531099 0.5000000 10  )=   4.187845                                   dl(    3.031099 0.5000000 10  )=   5.583793                                   dl(    3.531099 0.5000000 10  )=   6.979742                                   dl(    4.031099 0.5000000 10  )=   8.375691                                   dl(    4.531099 0.5000000 10  )=   9.771640                                   dl(    5.031099 0.5000000 10  )=  11.16759                                    dl(    5.531099 0.5000000 10  )=  12.56354                                    dl(    6.031099 0.5000000 10  )=  13.95948                                    gama(beta = 0.5000000                                                                       alfa = 15) >   1.071886                                         gama        beta      alfa                                                    dl(    1.071886 0.5000000 15  )=   0.0000000E + 00                            dl(    1.571886 0.5000000 15  )=   0.9000998                                  dl(    2.071886 0.5000000 15  )=   1.800200                                   dl(    2.571886 0.5000000 15  )=   2.700299                                   dl(    3.071886 0.5000000 15  )=   3.600399                                   dl(    3.571886 0.5000000 15  )=   4.500498                                   dl(    4.071886 0.5000000 15  )=   5.400597                                   dl(    4.571886 0.5000000 15  )=   6.300696                                   dl(    5.071886 0.5000000 15  )=   7.200796                                   dl(    5.571886 0.5000000 15  )=   8.100896                                   dl(    6.071886 0.5000000 15  )=   9.000996                                   gama(beta = 0.5000000                                                                       alfa = 20) >   1.133022                                         gama        beta      alfa                                                    dl(    1.133022 0.5000000 20  )=   0.0000000E + 00                            dl(    1.633022 0.5000000 20  )=   0.6427878                                  dl(    2.133022 0.5000000 20  )=   1.285576                                   dl(    2.633022 0.5000000 20  )=   1.928363                                   dl(    3.133022 0.5000000 20  )=   2.571151                                   dl(    3.633022 0.5000000 20  )=   3.213938                                   dl(    4.133022 0.5000000 20  )=   3.856726                                   dl(    4.633022 0.5000000 20  )=   4.499513                                   dl(    5.133022 0.5000000 20  )=   5.142301                                   dl(    5.633022 0.5000000 20  )=   5.785089                                   dl(    6.133022 0.5000000 20  )=   6.427876                                   gama(beta = 0.5000000                                                                       alfa = 25) >   1.219792                                         gama        beta      alfa                                                    dl(    1.219792 0.5000000 25  )=   0.0000000E + 00                            dl(    1.719792 0.5000000 25  )=   0.4807031                                  dl(    2.219792 0.5000000 25  )=   0.9614062                                  dl(    2.719792 0.5000000 25  )=   1.442109                                   dl(    3.219792 0.5000000 25  )=   1.922812                                   dl(    3.719792 0.5000000 25  )=   2.403515                                   dl(    4.219792 0.5000000 25  )=   2.884219                                   dl(    4.719792 0.5000000 25  )=   3.364922                                   dl(    5.219792 0.5000000 25  )=   3.845624                                   dl(    5.719792 0.5000000 25  )=   4.326327                                   dl(    6.219792 0.5000000 25  )=   4.807031                                   gama(beta = 0.5000000                                                                       alfa = 30) >   1.341506                                         gama        beta      alfa                                                    dl(    1.341506 0.5000000 30  )=   0.0000000E + 00                            dl(    1.841506 0.5000000 30  )=   0.3660255                                  dl(    2.341506 0.5000000 30  )=   0.7320511                                  dl(    2.841506 0.5000000 30  )=   1.098076                                   dl(    3.341506 0.5000000 30  )=   1.464102                                   dl(    3.841506 0.5000000 30  )=   1.830127                                   dl(    4.341506 0.5000000 30  )=   2.196153                                   dl(    4.841506 0.5000000 30  )=   2.562178                                   dl(    5.341506 0.5000000 30  )=   2.928203                                   dl(    5.841506 0.5000000 30  )=   3.294229                                   dl(    6.341506 0.5000000 30  )=   3.660254                                   gama(beta = 0.5000000                                                                       alfa = 35) >   1.515412                                         gama        beta      alfa                                                    dl(    1.515412 0.5000000 35  )=   0.0000000E + 00                            dl(    2.015413 0.5000000 35  )=   0.2782125                                  dl(    2.515413 0.5000000 35  )=   0.5564247                                  dl(    3.015413 0.5000000 35  )=   0.8346372                                  dl(    3.515413 0.5000000 35  )=   1.112849                                   dl(    4.015412 0.5000000 35  )=   1.391062                                   dl(    4.515412 0.5000000 35  )=   1.669274                                   dl(    5.015412 0.5000000 35  )=   1.947486                                   dl(    5.515412 0.5000000 35  )=   2.225699                                   dl(    6.015412 0.5000000 35  )=   2.503911                                   dl(    6.515412 0.5000000 35  )=   2.782123                                   gama(beta = 0.5000000                                                                       alfa = 40) >   1.776517                                         gama        beta      alfa                                                    dl(    1.776517 0.5000000 40  )=   0.0000000E + 00                            dl(    2.276517 0.5000000 40  )=   0.2069459                                  dl(    2.776517 0.5000000 40  )=   0.4138919                                  dl(    3.276517 0.5000000 40  )=   0.6208376                                  dl(    3.776517 0.5000000 40  )=   0.8277834                                  dl(    4.276517 0.5000000 40  )=   1.034729                                   dl(    4.776517 0.5000000 40  )=   1.241675                                   dl(    5.276517 0.5000000 40  )=   1.448621                                   dl(    5.776517 0.5000000 40  )=   1.655567                                   dl(    6.276517 0.5000000 40  )=   1.862513                                   dl(    6.776517 0.5000000 40  )=   2.069459                                   gama(beta = 0.5000000                                                                       alfa = 45) >   2.207107                                         gama        beta      alfa                                                    dl(    2.207107 0.5000000 45  )=   0.0000000E + 00                            dl(    2.707107 0.5000000 45  )=   0.1464467                                  dl(    3.207107 0.5000000 45  )=   0.2928933                                  dl(    3.707107 0.5000000 45  )=   0.4393399                                  dl(    4.207107 0.5000000 45  )=   0.5857866                                  dl(    4.707107 0.5000000 45  )=   0.7322332                                  dl(    5.207107 0.5000000 45  )=   0.8786799                                  dl(    5.707107 0.5000000 45  )=   1.025126                                   dl(    6.207107 0 5000000 45  )=   1.171573                                   dl(    6.707107 0.5000000 45  )=   1.318020                                   dl(    7.207107 0.5000000 45  )=   1.464466                                   gama(beta = 0.5000000                                                                       alfa = 50) >   3.054885                                         gama        beta      alfa                                                    dl(    3.054885 0.5000000 50  )=   0.0000000E + 00                            dl(    3.554885 0.5000000 50  )=   9.3198024E - 02                            dl(    4.054885 0.5000000 50  )=   0.1863960                                  dl(    4.554885 0.5000000 50  )=   0.2795941                                  dl(    5.054885 0.5000000 50  )=   0.3727920                                  dl(    5.554885 0.5000000 50  )=   0.4659900                                  dl(    6.054885 0.5000000 50  )=   0.5591879                                  dl(    6.554885 0.5000000 50  )=   0.6523860                                  dl(    7.054885 0.5000000 50  )=   0.7455839                                  dl(    7.554885 0.5000000 50  )=   0.8387819                                  dl(    8.054885 0.5000000 50  )=   0.9319797                                  gama(beta = 0.5000000                                                                       alfa = 55) >   5.559950                                         gama        beta      alfa                                                    dl(    5.559950 0.5000000 55  )=   0.0000000E + 00                            dl(    6.059950 0.5000000 55  )=   4.4910204E - 02                            dl(    6.559950 0.5000000 55  )=   8.9820325E - 02                            dl(    7.059950 0.5000000 55  )=   0.1347304                                  dl(    7.559950 0.5000000 55  )=   0.1796406                                  dl(    8.059951 0.5000000 55  )=   0.2245508                                  dl(    8.559951 0.5000000 55  )=   0.2694609                                  dl(    9.059951 0.5000000 55  )=   0.3143710                                  dl(    9.559951 0.5000000 55  )=   0.3592812                                  dl(   10.05995  0.5000000 55  )=   0.4041913                                  dl(   10.55995  0.5000000 55  )=   0.4491014                                  gama(beta = 0.6000000                                                                       alfa =  5) >   1.011504                                         gama        beta      alfa                                                    dl(    1.011504 0.6000000  5  )=   0.0000000E + 00                            dl(    1.511504 0.6000000  5  )=   2.272913                                   dl(    2.011504 0.6000000  5  )=   4.545825                                   dl(    2.511504 0.6000000  5  )=   6.818738                                   dl(    3.011504 0.6000000  5  )=   9.091650                                   dl(    3.511504 0.6000000  5  )=  11.36456                                    dl(    4.011504 0.6000000  5  )=  13.63748                                    dl(    4.511504 0.6000000  5  )=  15.91039                                    dl(    5.011504 0.6000000  5  )=  18.18330                                    dl(    5.511504 0.6000000  5  )=  20.45621                                    dl(    6.011504 0.6000000  5  )=  22.72912                                    gama(beta = 0.6000000                                                                       alfa = 10) >   1.047016                                         gama        beta      alfa                                                    dl(    1.047016 0.6000000 10  )=   0.0000000E + 00                            dl(    1.547016 0.6000000 10  )=   1.108010                                   dl(    2.047016 0.6000000 10  )=   2.216020                                   dl(    2.547016 0.6000000 10  )=   3.324029                                   dl(    3.047016 0.6000000 10  )=   4.432040                                   dl(    3.547016 0.6000000 10  )=   5.540050                                   dl(    4.047016 0.6000000 10  )=   6.648058                                   dl(    4.547016 0.6000000 10  )=   7.756068                                   dl(    5.047016 0.6000000 10  )=   8.864079                                   dl(    5.547016 0.6000000 10  )=   9.972089                                   dl(    6.047016 0.6000000 10  )=  11.08010                                    gama(beta = 0.6000000                                                                       alfa = 15) >   1.109838                                         gama        beta      alfa                                                    dl(    1.109838 0.6000000 15  )=   0.0000000E + 00                            dl(    1.609838 0.6000000 15  )=   0.7069143                                  dl(    2.109838 0.6000000 15  )=   1.413829                                   dl(    2.609838 0.6000000 15  )=   2.120744                                   dl(    3.109838 0.6000000 15  )=   2.827658                                   dl(    3.609838 0.6000000 15  )=   3.534573                                   dl(    4.109838 0.6000000 15  )=   4.241487                                   dl(    4.609838 0.6000000 15  )=   4.948401                                   dl(    5.109838 0.6000000 15  )=   5.655315                                   dl(    5.609838 0.6000000 15  )=   6.362230                                   dl(    6.109838 0.6000000 15  )=   7.069144                                   gama(beta = 0.6000000                                                                       alfa = 20) >   1.206618                                         gama        beta      alfa                                                    dl(    1.206618 0.6000000 20  )=   0.0000000E + 00                            dl(    1.706618 0.6000000 20  )=   0.4965974                                  dl(    2.206618 0.6000000 20  )=   0.9931949                                  dl(    2.706618 0.6000000 20  )=   1.489792                                   dl(    3.206618 0.6000000 20  )=   1.986390                                   dl(    3.706618 0.6000000 20  )=   2.482987                                   dl(    4.206618 0.6000000 20  )=   2.979584                                   dl(    4.706618 0.6000000 20  )=   3.476182                                   dl(    5.206618 0.6000000 20  )=   3.972780                                   dl(    5.706618 0.6000000 20  )=   4.469377                                   dl(    6.206618 0.6000000 20  )=   4.965974                                   gama(beta = 0.6000000                                                                       alfa = 25) >   1.349856                                         gama        beta      alfa                                                    dl(    1.349856 0.6000000 25  )=   0.0000000E + 00                            dl(    1.849856 0.6000000 25  )=   0.3623931                                  dl(    2.349856 0.6000000 25  )=   0.7247862                                  dl(    2.849856 0.6000000 25  )=   1.087179                                   dl(    3.349856 0.6000000 25  )=   1.449572                                   dl(    3.849856 0.6000000 25  )=   1.811965                                   dl(    4.349856 0.6000000 25  )=   2.174359                                   dl(    4.849856 0.6000000 25  )=   2.536751                                   dl(    5.349856 0.6000000 25  )=   2.899144                                   dl(    5.849856 0.6000000 25  )=   3.261538                                   dl(    6.349856 0.6000000 25  )=   3.623930                                   gama(beta = 0.6000000                                                                       alfa = 30) >   1.563856                                         gama        beta      alfa                                                    dl(    1.563856 0.6000000 30  )=   0.0000000E + 00                            dl(    2.063856 0.6000000 30  )=   0.2660254                                  dl(    2.563856 0.6000000 30  )=   0.5320508                                  dl(    3.063856 0.6000000 30  )=   0.7980763                                  dl(    3.563856 0.6000000 30  )=   1.064102                                   dl(    4.063856 0.6000000 30  )=   1.330127                                   dl(    4.563856 0.6000000 30  )=   1.596153                                   dl(    5.063856 0.6000000 30  )=   1.862178                                   dl(    5.563856 0.6000000 30  )=   2.128203                                   dl(    6.063856 0.6000000 30  )=   2.394229                                   dl(    6.563856 0.6000000 30  )=   2.660254                                   gama(beta = 0.6000000                                                                       alfa = 35) >   1.900716                                         gama        beta      alfa                                                    dl(    1.900716 0.6000000 35  )=   0.0000000E + 00                            dl(    2.400717 0.6000000 35  )=   0.1910401                                  dl(    2.900717 0.6000000 35  )=   0.3820800                                  dl(    3.400717 0.6000000 35  )=   0.5731202                                  dl(    3.900717 0.6000000 35  )=   0.7641601                                  dl(    4.400716 0.6000000 35  )=   0.9552000                                  dl(    4.900716 0.6000000 35  )=   1.146240                                   dl(    5.400716 0.6000000 35  )=   1.337280                                   dl(    5.900716 0.6000000 35  )=   1.528320                                   dl(    6.400716 0.6000000 35  )=   1.719360                                   dl(    6.900716 0.6000000 35  )=   1.910400                                   gama(beta = 0.6000000                                                                       alfa = 40) >   2.493007                                         gama        beta      alfa                                                    dl(    2.493007 0.6000000 40  )=   0.0000000E + 00                            dl(    2.993007 0.6000000 40  )=   0.1291597                                  dl(    3.493007 0.6000000 40  )=   0.2583195                                  dl(    3.993007 0.6000000 40  )=   0.3874791                                  dl(    4.493007 0.6000000 40  )=   0.5166388                                  dl(    4.993007 0.6000000 40  )=   0.6457986                                  dl(    5.493007 0.6000000 40  )=   0.7749582                                  dl(    5.993007 0.6600000 40  )=   0.9041179                                  dl(    6.493007 0.6000000 40  )=   1.033278                                   dl(    6.993007 0.6000000 40  )=   1.162437                                   dl(    7.493007 0.6000000 40  )=   1.291597                                   gama(beta = 0.6000000                                                                       alfa = 45) >   3.800942                                         gama        beta      alfa                                                    dl(    3.800942 0.6000000 45  )=   0.0000000E + 00                            d1)    4.300942 0.6000000 45  )=   7.5736046E - 02                            dl(    4.800942 0.6000000 45  )=   0.1514720                                  dl(    5.300942 0.6000000 45  )=   0.2272079                                  dl(    5.800942 0.6000000 45  )=   0.3029439                                  dl(    6.300942 0.6000000 45  )=   0.3786799                                  dl(    6.800942 0.6000000 45  )=   0.4544158                                  dl(    7.300942 0.6000000 45  )=   0.5301518                                  dl(    7.800942 0.6000000 45  )=   0.6058878                                  dl(    8.300942 0.6000000 45  )=   0.6816237                                  dl(    8.800942 0.6000000 45  )=   0.7573596                                  gama(beta = 0.6000000                                                                       alfa = 50) >   9.228890                                         gama        beta      alfa                                                    dl(    9.228890 0.6000000 50  )=   0.0000000E + 00                            dl(    9.728890 0.6000000 50  )=   2.7927648E - 02                            dl(   10.22889  0.6000000 50  )=   5.5855297E - 02                            dl(   10.72889  0.6000000 50  )=   8.3782844E - 02                            dl(   11.22889  0.6000000 50  )=   0.1117105                                  dl(   11.72889  0.6000000 50  )=   0.1396381                                  dl(   12.22889  0.6000000 50  )=   0.1675658                                  dl(   12.72889  0.6000000 50  )=   0.1954933                                  dl(   13.22889  0.6000000 50  )=   0.2234210                                  dl(   13.72889  0.6000000 50  )=   0.2513486                                  dl(   14.22889  0.6000000 50  )=   0.2792763                                  gama(beta = 0.7000000                                                                       alfa =  5) >   1.017952                                         gama        beta      alfa                                                    dl(    1.017952 0.7000000  5  )=   0.0000000E + 00                            dl(    1.517952 0.7000000  5  )=   1.699228                                   dl(    2.017952 0.7000000  5  )=   3.398454                                   dl(    2.517952 0.7000000  5  )=   5.097681                                   dl(    3.017952 0.7000000  5  )=   6.796908                                   dl(    3.517952 0.7000000  5  )=   8.496135                                   dl(    4.017952 0.7000000  5  )=  10.19536                                    dl(    4.517952 0.7000000  5  )=  11.89459                                    dl(    5.017952 0.7000000  5  )=  13.59381                                    dl(    5.517952 0.7000000  5  )=  15.29304                                    dl(    6.017952 0.7000000  5  )=  16.99227                                    gama(beta = 0.7000000                                                                       alfa = 10) >   1.074112                                         gama        beta      alfa                                                    dl(    1.074112 0.7000000 10  )=   0.0000000E + 00                            dl(    1.574112 0.7000000 10  )=   0.8200716                                  dl(    2.074112 0.7000000 10  )=   1.640143                                   dl(    2.574112 0.7000000 10  )=   2.460214                                   dl(    3.074112 0.7000000 10  )=   3.280286                                   dl(    3.574112 0.7000000 10  )=   4.100357                                   dl(    4.074112 0.7000000 10  )=   4.920428                                   dl(    4.574112 0.7000000 10  )=   5.740499                                   dl(    5.074112 0.7000000 10  )=   6.560570                                   dl(    5.574112 0.7000000 10  )=   7.380642                                   dl(    6.074112 0.7000000 10  )=   8.200713                                   gama(beta = 0.7000000                                                                       alfa = 15) >   1.176332                                         gama        beta      alfa                                                    dl(    1.176332 0.7000000 15  )=   0.0000000E + 00                            dl(    1.676332 0.7000000 15  )=   0.5137293                                  dl(    2.176332 0.7000000 15  )=   1.027459                                   dl(    2.676332 0.7000000 15  )=   1.541188                                   dl(    3.176332 0.7000000 15  )=   2.054917                                   dl(    3.676332 0.7000000 15  )=   2.568646                                   dl(    4.176332 0.7000000 15  )=   3.082376                                   dl(    4.676332 0.7000000 15  )=   3.596105                                   dl(    5.176332 0.7000000 15  )=   4.109834                                   dl(    5.676332 0.7000000 15  )=   4.623564                                   dl(    6.176332 0.7000000 15  )=   5.137293                                   gama(beta = 0.7000000                                                                       alfa = 20) >   1.341623                                         gama        beta      alfa                                                    dl(    1.341623 0.7000000 20  )=   0.0000000E + 00                            dl(    1.841623 0.7000000 20  )=   0.3504074                                  dl(    2.341623 0.7000000 20  )=   0.7008147                                  dl(    2.841623 0.7000000 20  )=   1.051222                                   dl(    3.341623 0.7000000 20  )=   1.401629                                   dl(    3.841623 0.7000000 20  )=   1.752036                                   dl(    4.341623 0.7000000 20  )=   2.102443                                   dl(    4.841623 0.7000000 20  )=   2.452851                                   dl(    5.341623 0.7000000 20  )=   2.803258                                   dl(    5.841623 0.7000000 20  )=   3.153665                                   dl(    6.341623 0.7000000 20  )=   3.504072                                   gama(beta = 0.7000000                                                                       alfa = 25) >   1.606009                                         gama        beta      alfa                                                    dl(    1.606009 0.7000000 25  )=   0.0000000E + 00                            dl(    2.106009 0.7000000 25  )=   0.2440831                                  dl(    2.606009 0.7000000 25  )=   0.4881659                                  dl(    3.106009 0.7000000 25  )=   0.7322490                                  dl(    3.606009 0.7000000 25  )=   0.9763318                                  dl(    4.106009 0.7000000 25  )=   1.220415                                   dl(    4.606009 0.7000000 25  )=   1.464498                                   dl(    5.106009 0.7000000 25  )=   1.708581                                   dl(    5.606009 0.7000000 25  )=   1.952664                                   dl(    6.106009 0.7000000 25  )=   2.196746                                   dl(    6.606009 0.7000000 25  )=   2.440830                                   gama(beta = 0.7000000                                                                       alfa = 30) >   2.054056                                         gama        beta      alfa                                                    dl(    2.054056 0.7000000 30  )=   0.0000000E + 00                            dl(    2.554056 0.7000000 30  )=   0.1660255                                  dl(    3.054056 0.7000000 30  )=   0.3320508                                  dl(    3.554056 0.7000000 30  )=   0.4980763                                  dl(    4.054056 0.7000000 30  )=   0.6641017                                  dl(    4.554056 0.7000000 30  )=   0.8301272                                  dl(    5.054056 0.7000000 30  )=   0.9961525                                  dl(    5.554056 0.7000000 30  )=   1.162178                                   dl(    6.054056 0.7000000 30  )=   1.328203                                   dl(    6.554056 0.7000000 30  )=   1.494229                                   dl(    7.054056 0.7000000 30  )=   1.660254                                   gama(beta = 0.7000000                                                                       alfa = 35) >   2.932765                                         gama        beta      alfa                                                    dl(    2.932765 0.7000000 35  )=   0.0000000E + 00                            dl(    3.432765 0.7000000 35  )=   0.1038678                                  dl(    3.932765 0.7000000 35  )=   0.2077354                                  dl(    4.432765 0.7000000 35  )=   0.3116030                                  dl(    4.932765 0.7000000 35  )=   0.4154705                                  dl(    5.432765 0.7000000 35  )=   0.5193383                                  dl(    5.932765 0.7000000 35  )=   0.6232059                                  dl(    6.432765 0.7000000 35  )=   0.7270735                                  dl(    6.932765 0.7000000 35  )=   0.8309411                                  dl(    7.432765 0.7000000 35  )=   0.9348087                                  dl(    7.932765 0.7000000 35  )=   1.038677                                   gama(beta = 0.7000000                                                                       alfa = 40) >   5.379220                                         gama        beta      alfa                                                    dl(    5.379220 0.7000000 40  )=   0.0000000E + 00                            dl(    5.879220 0.7000000 40  )=   5.1373534E - 02                            dl(    6.379220 0.7000000 40  )=   0.1027469                                  dl(    6.879220 0.7000000 40  )=   0.1541205                                  dl(    7.379220 0.7000000 40  )=   0.2054938                                  dl(    7.879220 0.7000000 40  )=   0.2568674                                  dl(    8.379220 0.7000000 40  )=   0.3082408                                  dl(    8.879220 0.7000000 40  )=   0.3596143                                  dl(    9.379220 0.7000000 40  )=   0.4109877                                  dl(    9.879220 0.7000000 40  )=   0.4623612                                  dl(   10.37922  0.7000000 40  )=   0.5137346                                  gama(beta = 0.7000000                                                                       alfa = 45) >   50.24860                                         gama        beta      alfa                                                    dl(   50.24860  0.7000000 45  )=   0.0000000E + 00                            dl(   50.74860  0.7000000 45  )=   5.0252676E - 03                            dl(   51.24860  0.7000000 45  )=   1.0050535E - 02                            dl(   51.74860  0.7000000 45  )=   1.5075803E - 02                            dl(   52.24860  0.7000000 45  )=   2.0101070E - 02                            dl(   52.74860  0.7000000 45  )=   2.5126338E - 02                            dl(   53.24860  0.7000000 45  )=   3.0151606E - 02                            dl(   53.74860  0.7000000 45  )=   3.5176873E - 02                            dl(   54.24860  0.7000000 45  )=   4.0202141E - 02                            dl(   54.74860  0.7000000 45  )=   4.5227408E - 02                            dl(   55.24860  0.7000000 45  )=   5.0252676E - 02                            gama(beta = 0.8000000                                                                       alfa =  5) >   1.030974                                         gama        beta      alfa                                                    dl(    1.030974 0.8000000  5  )=   0.0000000E + 00                            dl(    1.530974 0.8000000  5  )=   1.125542                                   dl(    2.030974 0.8000000  5  )=   2.251082                                   dl(    2.530974 0.8000000  5  )=   3.376623                                   dl(    3.030974 0.8000000  5  )=   4.502163                                   dl(    3.530974 0.8000000  5  )=   5.627705                                   dl(    4.030974 0.8000000  5  )=   6.753245                                   dl(    4.530974 0.8000000  5  )=   7.878787                                   dl(    5.030974 0.8000000  5  )=   9.004327                                   dl(    5.530974 0.8000000  5  )=  10.12987                                    dl(    6.030974 0.8000000  5  )=  11.25541                                    gama(beta = 0.8000000                                                                       alfa = 10) >   1.130530                                         gama        beta      alfa                                                    dl(    1.130530 0.8000000 10  )=   0.0000000E + 00                            dl(    1.630530 0.8000000 10  )=   0.5321329                                  dl(    2.130530 0.8000000 10  )=   1.064265                                   dl(    2.630530 0.8000000 10  )=   1.596398                                   dl(    3.130530 0.8000000 10  )=   2.128531                                   dl(    3.630530 0.8000000 10  )=   2.660663                                   dl(    4.130530 0.8000000 10  )=   3.192796                                   dl(    4.630530 0.8000000 10  )=   3.724929                                   dl(    5.130530 0.8000000 10  )=   4.257061                                   dl(    5.630530 0.8000000 10  )=   4.789194                                   dl(    6.130530 0.8000000 10  )=   5.321326                                   gama(beta = 0.8000000                                                                       alfa = 15) >   1.322975                                         gama        beta      alfa                                                    dl(    1.322975 0.8000000 15  )=   0.0000000E + 00                            dl(    1.822975 0.8000000 15  )=   0.3205443                                  dl(    2.322975 0.8000000 15  )=   0.6410881                                  dl(    2.822975 0.8000000 15  )=   0.9616324                                  dl(    3.322975 0.8000000 15  )=   1.282176                                   dl(    3.822975 0.8000000 15  )=   1.602720                                   dl(    4.322975 0.8000000 15  )=   1.923264                                   dl(    4.822975 0.8000000 15  )=   2.243809                                   dl(    5.322975 0.8000000 15  )=   2.564352                                   dl(    5.822975 0.8000000 15  )=   2.884897                                   dl(    6.322975 0.8000000 15  )=   3.205441                                   gama(beta = 0.8000000                                                                       alfa = 20) >   1.669916                                         gama        beta      alfa                                                    dl(    1.669916 0.8000000 20  )=   0.0000000E + 00                            dl(    2.169916 0.8000000 20  )=   0.2042170                                  dl(    2.669916 0.8000000 20  )=   0.4084340                                  dl(    3.169916 0.8000000 20  )=   0.6126506                                  dl(    3.669916 0.8000000 20  )=   0.8168676                                  dl(    4.169916 0.8000000 20  )=   1.021085                                   dl(    4.669916 0.8000000 20  )=   1.225302                                   dl(    5.169916 0.8000000 20  )=   1.429518                                   dl(    5.669916 0.8000000 20  )=   1.633735                                   dl(    6.169916 0.8000000 20  )=   1.837952                                   dl(    6.669916 0.8000000 20  )=   2.042169                                   gama(beta = 0.8000000                                                                       alfa = 25) >   2.344067                                         gama        beta      alfa                                                    dl(    2.344067 0.8000000 25  )=   0.0000000E + 00                            dl(    2.844067 0.8000000 25  )=   0.1257728                                  dl(    3.344067 0.8000000 25  )=   0.2515459                                  dl(    3.844067 0.8000000 25  )=   0.3773187                                  dl(    4.344068 0.8000000 25  )=   0.5030918                                  dl(    4.844068 0.8000000 25  )=   0.6288645                                  dl(    5.344068 0.8000000 25  )=   0.7546374                                  dl(    5.844068 0.8000000 25  )=   0.8804101                                  dl(    6.344068 0.8000000 25  )=   1.006183                                   dl(    6.844068 0.8000000 25  )=   1.131956                                   dl(    7.344068 0.8000000 25  )=   1.257729                                   gama(beta = 0.8000000                                                                       alfa = 30) >   4.029140                                         gama        beta      alfa                                                    dl(    4.029140 0.8000000 30  )=   0.0000000E + 00                            dl(    4.529140 0.8000000 30  )=   6.6025421E - 02                            dl(    5.029140 0.8000000 30  )=   0.1320508                                  dl(    5.529140 0.8000000 30  )=   0.1980761                                  dl(    6.029140 0.8000000 30  )=   0.2641015                                  dl(    6.529140 0.8000000 30  )=   0.3301269                                  dl(    7.029140 0.8000000 30  )=   0.3961523                                  dl(    7.529140 0.8000000 30  )=   0.4621775                                  dl(    8.029140 0.8000000 30  )=   0.5282030                                  dl(    8.529140 0.8000000 30  )=   0.5942284                                  dl(    9.029140 0.8000000 30  )=   0.6602538                                  gama(beta = 0.8000000                                                                       alfa = 35) >   14.74223                                         gama        beta      alfa                                                    dl(   14.74223  0.8000000 35  )=   0.0000000E + 00                            dl(   15.24223  0.8000000 35  )=   1.6695250E - 02                            dl(   15.74223  0.8000000 35  )=   3.3390671E - 02                            dl(   16.24223  0.8000000 35  )=   5.0085921E - 02                            dl(   16.74223  0.8000000 35  )=   6.6781171E - 02                            dl(   17.24223  0.8000000 35  )=   8.3476588E - 02                            dl(   17.74223  0.8000000 35  )=   0.1001718                                  dl(   18.24223  0.8000000 35  )=   0.1168671                                  dl(   18.74223  0.8000000 35  )=   0.1335623                                  dl(   19.24223  0.8000000 35  )=   0.1502578                                  dl(   19.74223  0.8000000 35  )=   0.1669530                                  gama(beta = 0.9000000                                                                       alfa =  5) >   1.071069                                         gama        beta      alfa                                                    dl(    1.071069 0.9000000  5  )=   0.0000000E + 00                            dl(    1.571069 0.9000000  5  )=   0.5518552                                  dl(    2.071069 0.9000000  5  )=   1.103712                                   dl(    2.571069 0.9000000  5  )=   1.655567                                   dl(    3.071069 0.9000000  5  )=   2.207422                                   dl(    3.571069 0.9000000  5  )=   2.759278                                   dl(    4.071069 0.9000000  5  )=   3.311134                                   dl(    4.571069 0.9000000  5  )=   3.862989                                   dl(    5.071069 0.9000000  5  )=   4.414845                                   dl(    5.571069 0.9000000  5  )=   4.966701                                   dl(    6.071069 0.9000000  5  )=   5.518556                                   gama(beta = 0.9000000                                                                       alfa = 10) >   1.319999                                         gama        beta      alfa                                                    dl(    1.319999 0.9000000 10  )=   0.0000000E + 00                            dl(    1.819999 0.9000000 10  )=   0.2441943                                  dl(    2.319999 0.9000000 10  )=   0.4883885                                  dl(    2.819999 0.9000000 10  )=   0.7325828                                  dl(    3.319999 0.9000000 10  )=   0.9767771                                  dl(    3.819999 0.9000000 10  )=   1.220971                                   dl(    4.319999 0.9000000 10  )=   1.465166                                   dl(    4.819999 0.9000000 10  )=   1.709360                                   dl(    5.319999 0.9000000 10  )=   1.953554                                   dl(    5.819999 0.9000000 10  )=   2.197748                                   dl(    6.319999 0.9000000 10  )=   2.441943                                   gama(beta = 0.9000000                                                                       alfa = 15) >   1.914492                                         gama        beta      alfa                                                    dl(    1.914492 0.9000000 15  )=   0.0000000E + 00                            dl(    2.414492 0.9000000 15  )=   0.1273588                                  dl(    2.914492 0.9000000 15  )=   0.2547180                                  dl(    3.414492 0.9000000 15  )=   0.3820768                                  dl(    3.914492 0.9000000 15  )=   0.5094356                                  dl(    4.414492 0.9000000 15  )=   0.6367944                                  dl(    4.914492 0.9000000 15  )=   0.7641537                                  dl(    5.414492 0.9000000 15  )=   0.8915125                                  dl(    5.914492 0.9000000 15  )=   1.018871                                   dl(    6.414492 0.9000000 15  )=   1.146230                                   dl(    6.914492 0.9000000 15  )=   1.273589                                   gama(beta = 0.9000000                                                                       alfa = 20) >   3.652381                                         gama        beta      alfa                                                    dl(    3.652381 0.9000000 20  )=   0.0000000E + 00                            dl(    4.152381 0.9000000 20  )=   5.8026921E - 02                            dl(    4.652381 0.9000000 20  )=   0.1160535                                  dl(    5.152381 0.9000000 20  )=   0.1740804                                  dl(    5.652381 0.9000000 20  )=   0.2321070                                  dl(    6.152381 0.9000000 20  )=   0.2901340                                  dl(    6.652381 0.9000000 20  )=   0.3481605                                  dl(    7.152381 0.9000000 20  )=   0.4061875                                  dl(    7.652381 0.9000000 20  )=   0.4642141                                  dl(    8.152381 0.9000000 20  )=   0.5222410                                  dl(    8.652381 0.9000000 20  )=   0.5802675                                  gama(beta = 0.9000000                                                                       alfa = 25) >   26.48351                                         gama        beta      alfa                                                    dl(   26.48351  0.9000000 25  )=   0.0000000E + 00                            dl(   26.98351  0.9000000 25  )=   7.4627930E - 03                            dl(   27.48351  0.9000000 25  )=   1.4925586E - 02                            dl(   27.98351  0.9000000 25  )=   2.2388378E - 02                            dl(   28.48351  0.9000000 25  )=   2.9851172E - 02                            dl(   28.98351  0.9000000 25  )=   3.7313964E - 02                            dl(   29.48351  0.9000000 25  )=   4.4776756E - 02                            dl(   29.98351  0.9000000 25  )=   5.2239552E - 02                            dl(   30.48351  0.9000000 25  )=   5.9702344E - 02                            dl(   30.98351  0.9000000 25  )=   6.7165136E - 02                            dl(   31.48351  0.9000000 25  )=   7.4627928E - 02  Z                         ______________________________________                                    

I claim:
 1. A method of creating a seal that is effective across a rangeof temperatures, including cryogenic temperatures, comprising the stepsof:a) selecting a sealing spacer having a desired coefficient of thermalexpansion and tube ends having different coefficients of thermalexpansion therefrom, said spacer and said tube ends also having shapescomplementary to each other such that when said tube ends are broughtinto contact with said spacer, a sealed sloped engagement resultsyielding sloped-surface sealing; and b) placing said spacer in contactwith said tube ends such that a sealed sloped engagement yieldingsloped-surface sealing is accomplished that maintains the seal across arange of various temperatures, including cryogenic temperatures.
 2. Themethod according to claim 1, wherein said sealing spacer is placed incontact with said tube ends by using a housing nut.
 3. The methodaccording to claim 2, wherein said housing nut, during cooling,contracts and thereby forces said tube ends toward each other, therebymaintaining the seal various temperatures, including cryogenictemperatures.
 4. The method according to claim 3, wherein said housingnut has a larger coefficient of thermal expansion than said tube ends.5. A method of joining tube ends to provide an effective seal across arange of temperatures, including cryogenic temperatures, wherein saidtube ends each have a sloped contact surface, said method comprising thesteps ofa) selecting a sealing spacer having a larger coefficient ofthermal expansion than said tube ends, and a shape complementarythereto; and b) placing said sealing spacer in contact with each saidsloped contact surface so that during cooling, as said sealing spacercontracts, a sealed engagement with each of said sloped contact surfacesyielding sloped-surface sealing is maintained.
 6. The method accordingto claim 5, wherein each of said sloped contact surfaces is on an outerportion of each of said tube ends.
 7. The method according to claim 6,wherein said sealing spacer is placed in contact with said slopedcontact surfaces by using a housing nut.
 8. The method according toclaim 7, wherein said housing nut, during cooling, contracts and therebyforces said tube ends toward each other, thereby maintaining theformation and maintenance of a leak-free seal at various temperatures,including cryogenic temperatures.
 9. The method according to claim 8,wherein said housing nut has a larger coefficient of thermal expansionthan said tube ends.
 10. The method according to claim 5, wherein saidsealing spacer is placed in contact with said sloped contact surfaces byusing a housing nut.
 11. The method according to claim 10, wherein saidhousing nut, during cooling, contracts and thereby forces said tube endstoward each other, thereby maintaining the formation and maintenance ofa leak-free seal at various temperatures, including cryogenictemperatures.
 12. The method according to claim 11, wherein said housingnut has a larger coefficient of thermal expansion than said tube ends.13. A cryogenic tube seal comprising a first coupling member having afirst sloped contact surface on an outer portion of said member; asecond coupling member having a second sloped contact surface on anouter portion of said member; and sealing means for establishing andmaintaining sloped-surface sealing between said coupling members atcryogenic temperatures at least as low as about 77K without resulting ininelastic deformation of either of said sloped contact surfaces or saidsealing means.
 14. The cryogenic tube seal, according to claim 13,wherein said sealing means comprises a sealing spacer having a greatercoefficient of thermal expansion than each of said coupling members,wherein said sealing spacer contacts said first contact surface and saidsecond contact surface, and wherein said sealing means also comprises ahousing nut selectively engaged with said first coupling member and saidsecond coupling member, wherein said housing nut has a greatercoefficient of thermal expansion than each of said coupling members. 15.The seal, according to claim 14, wherein said sealing spacer is anO-ring spacer.